Books - Ray Fu

Multivariable calculus.

Multivariable Calculus, Stewart. Standard lower-division undergraduate fare. The emphasis is on methods, rather than theory, and correspondingly there are many problems and few proofs. The sections on vector calculus I found somewhat weak.
div, grad, curl and all that, Schey. Short-ish book on the differential operators of vector calculus. The intuition is very good, but I thought the book dragged on considerably despite its short length.
Introduction to Electrodynamics, Appendix A, Griffiths. An appendix on the differential operators of vector calculus. The intuition is very good, and the exposition concise. This is a good refresher and elementary reference.
Advanced Calculus, A Geometric View, Callahan. Callahan takes a geometric approach to vector calculus, which is intuitive and a useful viewpoint. This text is considerably rigorous and assumes general mathematical maturity and some familiarity with linear algebra. Area is formalized as Jordan content, for me a novel approach.
Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Hubbard and Hubbard. I bought this book, and I liked the few parts I did read, but I haven't read it in enough detail to comment on it.

Overall comments: The first three suggestions are elementary. Stewart's main strength is as a problem book, and I found its similarity to high-school math textbooks quite comforting as a college freshman. I think Callahan would be a good second book on the subject if a rigorous understanding of multivariable calculus is desired. div, grad, curl is well liked by many, but I personally prefer the much shorter Appendix A of Griffiths. Several advanced mathematical textbooks like Hubbard and Hubbard cover multivariable calculus along with linear algebra and differential forms, and it might be useful to get a cohesive view of all these things.

Linear algebra.

Linear Algebra and Its Applications, Lay. Standard lower-division undergraduate fare. There is the same glut of problems but also a heavier emphasis on proofs than in Stewart's corresponding multivariable calculus text. The coverage of material is somewhat limited, as expected of an introductory text: topics like dual bases, Jordan normal form, generalized eigenvectors, and the spectral theorem are not covered. It isn't bad, but I didn't particularly like it, either.
Introduction to Linear Algebra, Strang. This is an interesting introductory linear algebra book. It also has a lot of problems, many less mechanical than those in Lay. The tone is relatively casual and the material presented in an intuitive fashion, but the pages feel cluttered---the theorem-proof style traditional to mathematics textbooks is integrated into the text and discussion here, an intentional stylistic choice, but one that makes navigation harder for me.
Linear Algebra, Friedberg. This was recommended to me by a graduate student. I haven't read it, but it looks nice.
Linear Algebra Done Right, Axler. The typesetting in this book is interesting, and there's a lot more color than I would expect from an upper-division book on linear algebra. Unlike Strang, this book closely adheres to the theorem-proof style and follows a rather curious determinant-free approach (hence "done right"). I found the definition of a quotient space unintuitive and stopped reading the book there.
Linear Algebra Done Wrong, Treil. There is opposition to Axler's approach. This advanced book is available freely on the author's website (Google it). It has tensors! I haven't read it, but thought it worth mentioning.

Overall comments: I have limited training in linear algebra, despite its relevance in the fields that I work with. One reason is that I can usually Google and understand the relevant linear algebra results quite easily, and another is that I simply don't like the material. I find a lot of the proofs quite abstract and hard to follow (or, for row-reduction proofs, too mechanical). For computer scientists, advanced linear algebra is absolutely crucial; for me, not so much---but who knows what I'm missing out on.

Differential equations.

An Introduction to Ordinary Differential Equations, Coddington. Standard lower-division undergraduate fare. The scope of the book is limited, but the presentation is done well. Answers to most exercises are at the end of the book.
Fundamentals of Differential Equations, Nagle, Saff and Snider. Standard lower-division undergraduate fare. The emphasis is on methods, rather than theory, and correspondingly there are many problems and few proofs. The material is an amalgam of the standard theory of ordinary differential equations and basic concepts in dynamical systems, integral transforms, and partial differential equations. Ch. 10 and 11, on partial differential equations, are dense and quite difficult to read.
Differential Equations with Applications and Historical Notes, Simmons. Standard textbook with a similar scope as Nagle, Saff, and Snider. The star is for the word problems at the end of Ch. 1, which are particularly good, and the introduction to the calculus of variations in Ch. 13.
Symmetry Methods for Differential Equations, Hydon. Applies Lie (group) theory to solve differential equations. The standard tricks---scalings, Möbius transformations, integrating factors, inspired substitutions, etc.---used for solving differential equations are collected under and understood from a group-theoretic viewpoint, and this book also serves as a short introduction to Lie groups. An introductory differential equations background is sufficient; the book presents a self-contained treatment of groups and the like, though at one point it does assume knowledge of the method of characteristics for partial differential equations. The presentation is fairly geometric. I liked the first part of the book, but got bored quite quickly after it started emphasizing theory rather than cool non-linear differential equations that I could solve. (Some notes: 1.)
Introduction to Symmetry Analysis, Cantwell. Intriguing book on my reading list.
Introduction to Partial Differential Equations, Olver. A standard upper-division textbook. I enjoyed the presentation and content, and the material is essentially self-contained, with mathematical maturity the only prerequisite.
Partial Differential Equations for Scientists and Engineers, Farlow. It does feel like an engineering textbook, whatever that means. The text is divided into many small lessons, each of which covers a particular concept or method of solving partial differential equations. I think this book works very well for a certain subset of people, which does not include me. While the partitioning of the text allows for very focused coverage of the material, it becomes harder to see the forest for the trees, and I quickly lost interest after the first few lesssons.
Partial Differential Equations, Evans. I was wondering what a graduate textbook on partial differential equations would look like, and now I know. I certainly don't know enough to comment on this book, and I have no intention to read it in detail.

Overall comments: Differential equations are quite fascinating, especially the nonlinear ones that look like they can't be solved but---surprise!---actually can be. The theory of ordinary differential equations is old, which I assume is why all the elementary ordinary differential equations textbooks, a la Coddington, feel like clones of each other. In the classic theory, the only nonlinear equations that are soluble are due to some inspired transform that linearizes the equation. The modern theory of differential equations, ordinary or otherwise, is based on Lie groups and Lie symmetries, wherein a differential equation is solved by studying its symmetries (Hydon, Cantwell). Start with Simmons, then, based on interest, either Hydon or Olver. Read Farlow before Olver if it helps you.

Real analysis.

Understanding Analysis, Abbott. This is the only real analysis book that has kept my interest long enough to finish. The material is introductory and the breadth of topics allegedly quite limited, though my limited knowledge of real analysis does not allow me to comment. I found Ch. 3, on topology, quite difficult. (Some disjoint notes: 1, 2.)

Overall comments: I simply don't find this subject interesting, although it is important enough that I've spent some effort to try to learn it. In theory it's supposed to form the basis of more advanced mathematical coursework, but I've gotten by for the most part.

Complex analysis.

Complex Variables and Applications, Brown and Churchill. A standard introduction to complex analysis. The material is partitioned into many small sections, and Brown and Churchill do a good job motivating and presenting the material. The coverage is relatively standard but done very well, and the proofs are relatively simple to comprehend. Some familiarity with multivariable calculus is sufficient as prerequisite; no real analysis is needed.
Visual Complex Analysis, Needham. Complex analysis from a geometric viewpoint. Complex-analytic functions are very "nice" mathematically, with rich geometric structure. Two particularly vivid examples are the representation of complex differentiation as an "amplitwist"---a scaling combined with a rotation---and the geometric integration of \(z^n\) over the unit circle for integral \(n\), which gives insight as to why the integral should vanish for all but \(n = -1\).

Overall comments: Unlike real analysis, this is a very interesting subject, primarily because holomorphic functions, the primary objects of study in complex analysis, are a much nicer set of functions than real functions in general. Complex analysis also has a geometric flavor and very good textbooks that make use of it. Reading Needham and Brown and Churchill together gave me a very complete understanding and intuition for the subject.

Discrete mathematics.

Concrete Mathematics, Graham, Knuth, and Patashnik. A rather unique book with topics from continuous and discrete mathematics: sums, number theory, and generating functions. The introductory chapter was a much harder read than the next few chapters. Full solutions to problems (hard!) are provided at the end of the book. Mathematical maturity is the only prerequisite, but discrete mathematics requires a different way of thinking, which took me a while to get used to.
Generatingfunctionology, Wilf. Wilf's passion for generating functions is infectious, and the manipulations by which generating functions can be derived and put to use are fascinating. The first three chapters don't require any mathematical knowledge past Taylor series, but the last two chapters get quite hard. Full solutions to problems are provided at the end of the book.

Overall comments: Discrete mathematics is blessed with a number of good textbooks. Concrete Mathematics and generatingfunctionology have essentially no prerequisites and are both good reads. They present useful techniques for studying sums, generating functions, and recursion relations, all of which have come in handy for me.

Probability and stochastic processes.

Weighing the Odds, Williams. Currently reading. By the same invigorating author of Probability with Martingales (see below), an introductory book on probability! Williams writes very compellingly, and his conversational style, appropriate use of emphasis, and focus on intuition rather than rigor make this a very useful book for a beginning student. The paradoxes so prevalent in probability, fueled by often incorrect intuition, are presented in a very clear manner.
Stochastic Processes and Models, Stirzaker. Simplified introduction to probability and stochastic processes that doesn't (!) require a background in real analysis or measure theory. Considerable number of results are stated without proof or proven in weaker forms. Solutions are provided to a significant number of the harder problems and exercises. I found the end-of-chapter exercises considerably harder than the end-of-section problems. (Notes: 1. I spent some time elaborating on convergence of different types, which I felt was covered quite superficially, then realized that it was probably because that material was relatively unimportant.)
Probability and Random Processes, Grimmett and Stirzaker. Covers the content of Stochastic Processes and Models in considerably more detail and rigor.
Probability with Martingales, Williams. A pared-down version of Grimmett and Stirzaker that emphasizes the theory of martingales. The text is designed for a mathematically inclined reader experienced with measure theory, but I found it lucid even without such a background. The notation and typesetting are interesting and remind me of Strang's Linear Algebra.
An Introduction to Stochastic Differential Equations, Evans. Designed for senior undergraduates, and hence formulated in a non-rigorous manner. As far as I can tell, the emphasis is on the intuition behind the main concepts of stochastic differential equations, and proofs are secondary. To get a full coverage of stochastic calculus probably requires pairing this text with one of the subsequent options.
Elementary Stochastic Calculus with Finance in View, Mikosch. An introduction to stochastic calculus targeted to financial analysis. The financial interpretation is largely left to a final chapter, and the rest of the text can be read independently.
Introduction to Stochastic Calculus with Applications, Klebaner. Another introduction to stochastic calculus.

Overall comments: A lot of books on probability and stochastic processes purport to be introductory; I chose Stochastic Processes and Models because it doesn't discuss \(\sigma\)-algebras in the context of probability spaces or filtrations in the context of martingales---super-introductory, if you will. My goal was simply to survey the field and not be subject to a rigorous introduction, but such a text is surprisingly hard to find. The same problem occurs with stochastic calculus and stochastic differential equations, but I have listed those which I believe elementary.

Tensor analysis and differential geometry.

Introduction to Tensor Analysis, Grinfeld. A gentle introduction to tensor analysis. The tensor notation is introduced gradually, and the various conventions neatly fall into place. Intuition is emphasized. Grinfeld also discusses the interesting Voss-Weyl formula, which allows for simple evaluation of the divergence in arbitrary coordinate systems, but I have not seen this formula so called anywhere else. The book does have a number of small errors, however, and the contravariant surface basis in Ch. 12 does not seem to have been explicitly defined. (Some notes: 1. I derive representations for the covariant derivative for tensors of arbitrary order by introducing the tensor product and proving that the product rule of calculus holds for it.)
An Introduction to Tensors and Group Theory for Physicists, Jeevanjee.
Differential Geometry, Kreyszig. An introduction to differential geometry proper. Kreyszig writes lucidly, and the book proceeds naturally from curves to surfaces to tensor analysis, though I was still uncomfortable with tensors and index manipulations before reading Grinfeld. The material is partitioned into small sections, and full solutions to problems are provided at the end of the book. Most are doable with results and information from each section, though some problems require external knowledge. (Some notes: 1.)
A Short Course in Differential Geometry and Topology, Fomenko and Mishchenko. I haven't progressed far enough with this book to comment upon its content, but Fig. 1.6 shows a smooth mapping turning a giraffe into a hippopotamus.

Overall comments: Most texts on differential geometry and tensor calculus are written for mathematicians and most physics textbooks seem to just introduce them as needed, which makes it hard to find independent resources for these fields. Nevertheless, here are some options. Grinfeld and Kreyszig require knowledge of multivariable calculus, Jeevanjee of linear algebra. Fomenko and Mishchenko is more mathematically inclined, but it remains lucid and emphasizes geometric intuition.

Group theory.

Lie Groups, Lie Algebras, and Representations, Hall. Hey, a group theory book that's actually interesting to me! Still reading, review pending.

Overall comments: Group theory is one of those fields that are relevant to me but that I've never found a good reference for. The fundamentals of group theory are straightforward enough, I think, but the presentation has always felt boring and strained to me. There are also other fields of mathematics of less interest to me, but which a "good" book is generally known: Dummit and Foote in abstract algebra, Munkres in topology, Hardy in number theory.

Miscellaneous math.

Street-Fighting Mathematics, Mahajan. An analysis of problems through approximations, pictorial approaches, dimensional analysis, and analogies. The problems covered are not particularly hard, but are made much more obvious from a geometric viewpoint, and often succumb to simple approximations. This book describes less a bag of tricks and more a useful mindset for tackling problems, and is particularly helpful for beginning students.
The Mathematical Mechanic, Levi. Standard problems in mathematics are solved using physical principles, which is quite refreshing. The book is simple to pick up, and the physical analogues of mathematical problems are didactic. For example, a physical proof of the \(n^\text{th}\) roots of unity summing to zero for any integer \(n\) can be visualized as an object in the center of a circle being pulled in \(n\) different directions equally spaced about the circle; geometrically, we see that the forces are evenly distributed and that the object will not move, so the sum of the forces---the sum of the roots---must be zero.
Inside Interesting Integrals, Nahin. Fascinating book of tricks for solving integrals: symmetry, clever \(u\)-substitution, power-series solutions, reduction through recurrence relations, special functions, differentiation under the integral sign, contour integration. Nahin's interest in the subject is evident, and the book is a relatively easy read. A lot of the text is dedicated to working out quite complicated integrals, and it is worth trying to solve a presented integral before reading the solution.
The Knot Book, Adams. I don't personally like knots, but this is supposedly a good book for those who do. It's nice to see that something so ingrained in physical reality can actually be well formulated as a mathematical theory.

Overall comments: Just a few interesting books on more esoteric topics, reflecting my own interest in physics-y math tricks (or is it mathy physics tricks?) and solving integrals.

This concludes the math section of this book list; the rest is physics and chemistry. Mathematics books make up the bulk of this list because all my math past ordinary differential equations is self-taught, whereas a significant part of my chemistry and physics knowledge comes from coursework.

Classical and analytical mechanics.

Introduction to Classical Mechanics, Morin. Two stars for the problems. Morin spends just enough time on expositions and the rest on problems, solutions, and exercises. Other introductory books lack the same emphasis on problem-solving and the quality and number of examples and problems presented. Tricky points are highlighted and discussed extensively---Morin has a section in the appendix for subtle issues with problems with varying mass, as well as a detailed discussion of physical models for falling chains. There is also a full solutions manual for the exercises floating around the Internet, which I have found very useful.
Classical Mechanics, Kibble and Berkshire. Standard development of classical mechanics, somewhat beyond an introductory book but not too advanced. The book is quite concise and interesting to read. Points of subtlety are often discussed clearly but not emphasized, so many passages have to be read multiple times. I did not lose interest in this book, as I did with so many other mechanics textbooks. There are both numerical and theoretical problems that span a good range of difficulty, and numerical answers (but not solutions) are provided at the end of the book. I especially liked Ch. 6, on potential theory, and Ch. 14's discussion of action-angle variables.
Structure and Interpretation of Classical Mechanics, Sussman and Wisdom. Free online. This book provides a curiously programmatic approach to classical mechanics---the well-read reader might know Structure and Interpretation of Computer Programs, off of which the title of this book was based. As with Farlow (above in differential equations), I think this book is well suited to a group of people that does not include me. The idea is that, to understand classical mechanics and actually carry out computations in the subtle Lagrangian framework, the gold standard is to be able to program the equations, and that is what this book espouses. I learned that derivatives should really be noted by the index of the variable differentiated, not by the variable itself, but have since shrugged that off for the usual notation.
New Foundations for Classical Mechanics, Hestenes. Aside from performing influential work in physics education, Hestenes also advanced a theory of geometric algebra, a framework that would extend and replace Gibbs' vector analysis. This book recasts classical mechanics with this geometric framework. What I took away from this perspective was that the strange pseudovectors or axial vectors of Gibbs should really be thought of as bivectors of geometric algebra, but it seems to me that the advantages of the geometric framework are insufficient for replacing the Gibbsian framework that has so pervaded modern science.
Geometric Mechanics, Holm. Another treatment of geometric mechanics.
Mechanics, Landau and Lifshitz. This book is surprisingly thin for its remarkable insight. The development is quite concise and not particularly beginner-friendly---the first few pages present a variational approach to mechanics starting with Hamilton's principle of extremal action, and the lack of instruction regarding the mathematical manipulations of variations was quite frustrating the first few times I read it. Nevertheless, with a good foundation in classical mechanics, this is a good next step. Sec. 10, on mechanical similarity, was something I had not seen elsewhere, and the geometric development of two-body collisions in Sec. 17 simplifies the topic considerably.
Classical Dynamics, José and Saletan. This is a big book with a geometric emphasis. At the time I was not so enamored with classical mechanics that I wanted to read the whole thing.

Overall comments: Classical mechanics, this oldest branch of physics, does not lack for textbooks. It was still hard for me to find a textbook that I enjoyed, however, possibly because the history of classical mechanics also implies a rigidity of the curriculum. The standard graduate reference is Goldstein, which I have refrained from including on this list because I was so frustrated with the book in Ch. 1 alone that I stopped reading. I think there are much better books out there, but I suppose there must be a reason Goldstein is standard.

Electricity and magnetism.

Electricity and Magnetism, Purcell. A classic book in electromagnetic theory. Essentially no prerequisites but mathematical and physical maturity, and I think the multivariable calculus necessary for electricity and magnetism is self-contained in the book. Ch. 5, which shows how the electric and magnetic field are intertwined by special relativity, is worth a ★ of its own. Unfortunately, I haven't read enough of this book to comment further.
Introduction to Electrodynamics, Griffiths. A standard introduction to electrostatics and electrodynamics. A background in multivariable calculus is recommended, though Griffiths does provide a concise self-contained treatment of the required mathematics. Griffiths' tone is rather conversational, which can be off-putting to some readers---I found his quantum mechanics book very annoying to read, but I actually like his electrodynamics text. There is a strong emphasis on intuition and physical understanding, and Griffiths does a very good job of communicating important but subtle concepts to the reader. Appendix A discusses vector calculus and is a good, concise reference. (Some notes: 1.)
Static and Dynamic Electricity, Smythe. The preface is...interesting. Supposedly there are good problems in this book, and the electric field of an ellipsoid was first derived here, along with other significant results. I was not sufficiently interested in the topic to read more than the first chapter, but I think it could be a valuable perspective.
Modern Electrodynamics, Zangwill. Graduate electromagnetism text. It is long, long, long. I paged through it briefly and found the writing clear and compelling, though I'm not sure how that view will change if I tried sitting down and doing the problems and actually learning.
Classical Electrodynamics, Jackson. Oof. This is the standard graduate electromagnetism text, and has a reputation for having very hard problems. I haven't read it, but, if you want to, well, good luck.

Overall comments: There seem to be only a few standard textbooks in electricity and magnetism, but all of them are very good. Smythe is non-standard, so I had a hard time tracking down a physical copy.

Quantum mechanics.

Principles of Quantum Mechanics, Shankar. I haven't read much of this book, but Shankar has a good reputation for being didactic, and the small parts of this book that I did read were quite easy to follow.
Introduction to Quantum Mechanics, Griffiths. I don't like this book, but it is popular enough that I should mention it. Griffiths' tone is conversational and verges into the annoying for me, and I find his treatment of the material hard to follow. The exposition of the Schrödinger equation and related manipulations in Ch. 1 feels particularly dense, and I don't understand why it is presented so early.
Quantum Mechanics, Zettili. An introductory quantum mechanics book that doubles as a book of problems, much in the same vein as Morin's Classical Mechanics. The theoretical aspects of quantum mechanics is covered somewhat weakly, and much of the treatment has an operational flavor (these are the rules, these are the standard computations, now just use them) that is not theoretically motivated. The main strength is the large number of examples and problems.
Quantum Mechanics: A Modern Development, Ballentine. Advanced text for a second look at quantum mechanics. The emphasis is on the theoretical development of quantum mechanics, and Ballentine presents these insights in a very clear manner. The coverage is spotty, in the sense that this is more like a coverage of special topics in quantum mechanics rather than a traditional textbook, however, and this should not be used as a primary text.
Quantum Mechanics, Littlejohn. Course notes for Physics 221A-B at UC Berkeley, available online. I had the good fortune of auditing the class, and Littlejohn is a wonderful lecturer with correspondingly good lecture notes. They remain the best theoretical treatment of the subject that I know of, and I wish I had the time to take more classes with him. I did lose interest in the course when he started covering relativistic quantum mechanics and second quantization, but that's on me.

Overall comments: There are a lot of quantum mechanics textbooks out there, but I don't like most of them for one reason or another. I have yet to find a satisfactory elementary coverage of quantum mechanics, but Shankar might be a good read. Zettili is good for problems and for understanding how to do the calculations, but it should be paired up with a more theoretical treatment---at least Littlejohn's Notes 1. Ballentine is a fun read with advanced topics that might not make much sense initially.

Thermodynamics and statistical mechanics.

An Introduction to Thermal Physics, Schroeder. An intuitive introduction from a physical perspective. The coverage is limited, but whatever is covered is done so well.
Thermodynamics and an Introduction to Thermostatistics, Callen. My favorite textbook. I don't think there's a better thermodynamics book out there, or one that can give significantly more perspective on the material than Callen already has. The preface, introduction, and Ch. 21 are sublime: they discuss the foundation of thermodynamics in symmetry, and the special symmetry that certain dynamical modes possess that allow them to exist even in the thermodynamic limit. This is a viewpoint that I have not found in any other text. Thermodynamics is a subtle subject, but Callen's treatment is clear, compelling, and comprehensive. I have not found elsewhere the Le Chatelier-Braun principle (which differs from the standard Le Chatelier principle) and its proof. The statistical thermodynamics chapters are still good, especially the first few, but do not compare to his thermodynamics ones.
Engineering and Chemical Thermodynamics, Koretsky. A chemical engineering viewpoint on thermodynamics, which means significant emphasis on open systems, energy balances, and the thermodynamics of mixtures, all of which are often not covered or emphasized in the chemistry curriculum. (There was a question (multiple-choice, five options) on the chemistry GRE on the low-pressure limit of fugacity, and only 15% of students got it right.) The development of these concepts and applications is lucid, and for engineering purposes this is sufficient, but I think this is an incomplete treatment of thermodynamics that must be supplemented by, say, the theoretical treatment of Callen.
An Introduction to Statistical Mechanics, Hill. A comprehensive introduction from a chemical perspective. After introducing the theory, the rest of the book essentially studies a wide range of chemical examples and applications. I found the first few chapters on parallels and connections between statistical mechanics and thermodynamics quite revealing.
Concepts in Thermal Physics, Blundell and Blundell. Used to be my favorite textbook. The material is divided into concise chapters with interesting end-of-chapter problems, and briefly covers a very wide range of supplementary material. I have not found their argument for deriving the Gibbs entropy formula presented elsewhere, and I was quite surprised to find non-equilibrium topics like Brownian motion and Onsager's reciprocal relations covered. Some of the problems were quite difficult my first time through, though careful perusal of the chapter provides sufficient information for solving them.
Statistical Thermodynamics, Fowler and Guggenheim. This is an old reference book, and there seems to be a significant divide between classical and modern statistical mechanics, so much of the material of this text was new to me despite my coursework and own reading. Many sections simply detail the application of the standard machinery of statistical mechanics (find the partition function, then the relevant thermodynamic quantities) for physical systems of interest, and I particularly liked the treatment of hydrogen, which requires quantum mechanics.
Introduction to Modern Statistical Mechanics, Chandler. A modern perspective on statistical mechanics, better used as a second course, rather than an introduction, on statistical mechanics. The development is formal and centered around the second law, introduced as a postulate of maximum entropy. The topics covered are somewhat more advanced than those in the previous books, and the discussion of phase transitions was particularly insightful. On the other hand, the book is terse and important points are often left for the reader to discover.
Excursions in statistical dynamics, Crooks. A PhD thesis that serves as a friendly introduction to stochastic thermodynamics and non-equilibrium statistical mechanics, written by the same person for whom the Crooks fluctuation theorem is named. I found the figures and illustrations apt, and the notation and terminology precise and clear. Results of far-reaching scope seem to be derived quite naturally from simple equations and manipulations, the hallmark of clarity.
The large deviation approach to statistical mechanics, Touchette. A review article on large deviation theory available on arXiv. Large deviation theory is, as I now believe, the proper mathematical formulation of thermodynamics and statistical mechanics, and generalizes also to the non-equilibrium regime. This theory focuses on the statistics and distributions of exponentially rare random variables, and Touchette's review is a surprisingly accessible introduction to this rather specialized subject.

Overall comments: There are a lot of books on statistical mechanics, with several distinctive perspectives. This subject has elements of both physics and chemistry, and the differing viewpoints of the two sciences leads to an interesting medley of topics all under the umbrella of statistical mechanics. This is the field I work on, so I've read a lot more of these books. Callen has all you need to know about thermodynamics; for statistical mechanics, I have not found a flawless elementary treatment. I would probably couple Blundell and Blundell with Hill, followed by some looks at Fowler and Guggenheim and Chandler.

Soft condensed matter physics.

Soft Condensed Matter, Jones. A survey of topics in soft condensed matter---colloids, polymers, gels, liquid crystals, self-assembly, and proteins---and one that describes the essence of each subfield in a compelling fashion. The mathematics is neither the main focus nor main draw of the book, and I simply oohed and aahed at the equations as I read.
Polymer Physics, Rubinstein. Didactic introductory textbook on polymers with insights not available in more advanced treatments.
Scaling Concepts in Polymer Physics, de Gennes. This was an enlightening but very frustrating textbook. The bulk of polymer physics is well treated by scaling laws, polymer chains being self-similar within characteristic length scales. The last chapter, on the analogy between excluded-volume polymer chains and a magnetic spin system, was fascinating. Most of the equations in de Gennes reflect this emphasis on scaling and are only correct up to a multiplicative constant. I think you can probably count on your fingers the number of times actual equalities appear in the text. de Gennes has strong physical intuition, and much of my frustration arises because he thinks it obvious that something is true, and it certainly does not appear so to me.
Introduction to Polymer Physics, Doi. A highly mathematical treatment of the subject, which complements de Gennes well.
Principles of Condensed Matter Physics, Chaikin and Lubensky. A conceptual framework for soft condensed matter physics. The mathematical maturity required is quite high---there are frequently places where the reader is expected to fill in a number of steps in a derivation. There is an introduction to Fourier transforms and functional derivatives when they first occur, but the treatment is too limited for a first exposure. There are challenging problems. While it offers important insights, much of this book remains impenetrable to me.

Overall comments: Soft condensed matter physics is a popular field nowadays, and one that is particularly relevant to my work. Jones is a good starting point, followed by Rubinstein if polymers are of interest. Doi and de Gennes can be read simultaneously, and I think the counterpoint between the mathematical and the intuitive physical treatment is quite interesting. Chaikin and Lubensky is the next step up from Jones, but it's a very tall step.

Hard condensed matter physics. (Solid-state physics.)

Oxford Solid State Basics, Simon. An elementary treatment of solid-state physics that provides intuition and a concise description of the main ideas.
Solid State Physics, Ashcroft and Mermin. A comprehensive treatment of solid-state physics, although somewhat dated. There is a new revised edition which I did not particularly like---the English appears unedited, a remarkable oversight for a book of this caliber.

Overall comments: I read Ashcroft and Mermin before Simon, and I feel like this order did help me consolidate and refine my understanding of the material by focusing on the most important results, though it seems like going from Simon to Ashcroft and Mermin should be the natural progression.

Hydrodynamics.

An Album of Fluid Motion, Van Dyke. The rare technical book that nevertheless fits on a coffee table. This book contains black-and-white photographs of fluid flow in different contexts and environments, possessing both high visual appeal and a wealth of technical information. I enjoyed looking at this book alongside a more conventional hydrodynamics textbook for its beautiful examples of fluid flow.
A Gallery of Fluid Motion, Samimy, Breuer, Leal, and Steen. Like the above book, but more recent, in color, and with more description.
Physical Hydrodynamics, Guyon, Hulin, Petit, and Mitescu. I found this book strangely appealing despite its standard coverage of topics in hydrodynamics. The illustrations are particularly relevant and well-made, and I found the flow and style of the book instructive and very easy to follow. I preferred the typesetting of the first edition to the second, although the second does contain updated coverage of turbulence.
Hydrodynamics, Lamb. A treatise of classical hydrodynamics with encyclopedic coverage, the first edition of which was published in 1879 (!). The book is divided into small sections which cover, in the traditional style, a topic apiece. There is significant emphasis on solving difficult partial differential equations in hydrodynamics.

Overall comments: Hydrodynamics is an interesting subject. The classical treatment emphasizes solving for the fluid flow through a large number of systems, making heavy use of the theory of partial differential equations in a manner similar to that in electrodynamics. I find the statistical perspective of hydrodynamics particularly illuminating: hydrodynamics is a close cousin to thermodynamics in the sense that it also deals with a large number of degrees of freedom, most of which are integrated out upon coarse-graining. Unlike thermodynamics, however, the systems in hydrodynamics are mobile and possess both linear and angular momentum, and it is these momenta that we solve for in the classical treatment. Physical Hydrodynamics, coupled with An Album of Fluid Motion, forms a good starting point.

Molecular and cellular biology.

The Machinery of Life, Goodsell. The material in this book is fairly basic---at least based on the little I know of molecular biology---but is coupled with detailed illustrations that really provide perspective into things. It remains the only book in biology that has interested me enough to finish.
Molecular Biology of the Cell, Alberts, Johnson, Lewis, Raff, Roberts, and Walter. Standard reference that is long but apparently well liked.
Physical Biology of the Cell, Phillips, Kondev, Theriot, and Garcia. Standard biophysics (well, physical biology...) reference.

Overall comments: I never used to find molecular biology interesting, but perhaps it's because I never found a good starting point. Goodsell's The Machinery of Life was very readable and interested me enough to want to proceed further.