Learning recommendations

Here I make a list of books and lecture notes that I have read, skimmed through, or sometimes even just a chapter within, so long as they have helped me in some way. I review the books I read regularly on Goodreads, and I compile here the list by subject matter so that other people (especially students like me) may hopefully benefit from them.

Disclaimer: the review/opinion is there mainly to guide others who may read books with different style or focus or needs. Please treat them as that — opinions (of a single graduate student), and not e.g. as some sort of endorsement to purchase the books.

Remark: I hope to improve this page one day (6 March 2023).

General Relativity (GR)

1. General Relativity (Robert Wald)
   Classic reference. It is actually not very useful in my opinion unless you already know enough GR, but useful as a go-to when you want to find a particular subject matter since it covers pretty much every advanced topic.

2. First Course in General Relativity (Bernard Schutz)
   Very useful and not too-watered down introductory text. I recommend reading this for first-timer.

3. General Relativity (Harvey S. Reall)
   This is actually a set of lecture notes from DAMTP. For second reading in GR (e.g. after Schutz) or first reading if you are confident with facing more mathematics. So far this is the best place to learn advanced GR for me, with clean derivations and calculations. Has nice illustrations on calculations involving normal coordinates.

4. General Relativity - An Introduction for Physicists (Anthony N. Lasenby, George Efstathiou, M. P. Hobson)
   Some computations here are very explicit. The only issue is that this is one of the very few books I know in GR that uses mostly minus signature for the metric. However, it has the advantage that it keeps all the fundamental constants like G and c explicit.

5. A Relativist's Toolkit (Eric Poisson)
   Contain very detailed, practical techniques such as ADM decomposition and congruences.

6. Exact Space-Times in Einstein's General Relativity (Jerry B. Griffifths, Jiri Podolski)
   Comprehensive collections of (3+1) dimensional spacetimes and their properties.

7. Advanced Lectures on General Relativity (Geoffrey Compere)
   Covers advanced topics that are not in standard texts but nonetheless important for the frontier such as surface charges and BMS symmetry. It is also short with detailed information about external references.

Quantum field theory

1. Quantum Field Theory for the Gifted Amateur (Tom Lancaster, Stephen J. Blundell) Conceptually useful for beginners, and quite accurate. Excludes very technical computations such as LSZ reduction formula, but otherwise quite comprehensive and covers a lot of topic.

2. Quantum Field Theory and the Standard Model (Matthew D. Schwartz) Currently my favourite book. It covers and explains, albeit often "hand-wavingly", many concepts otherwise not covered in many texts. It is also comprehensive and broken into good-sized chapters.

3. Quantum Field Theory (Lewis Ryder) Another favourite book, because the prose is very clear (at least for first three chapters anyway) and focuses on path integral methods. Main "drawback" (or not) is that it has no real exercises, but otherwise it fleshes out a lot of detailed calculations. Should complement with other sources.

4. Quantum Field Theory (David Tong) Another excellent set of lecture notes from DAMTP. No exercises either, but very clear for conceptual aspects of QFT. Very useful to complement with other textbooks.

Quantum field theory in curved spacetime

1. Quantum Fields in Curved Spaces (N. D. Birrell, P. C. W. Davies)
   Classic, though a bit old and somewhat hard to read for first time readers; complement to more modern review papers. I have read the first five chapters for my qualifying examinations, and I think one can learn a lot from this book in terms of conceptual aspects and the mechanics, but I did not feel like I could do much in terms of explicit calculations except in the simplest of examples.

2. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Robert Wald)
   Very difficult but very insightful, based on algebraic quantum field theory framework. It discusses the subject from unusual angles, e.g. quantization with respect to null hypersurfaces, or the use of symmetric bilinear form $\mu$ and symplectic form $\Omega$ (which implies a complex structure $J$ that naturally splits modes into positive and negative frequencies).

3. Introduction to Quantum Effects in Gravity (S. Winitzky, V. P. Mukhanov)
   Very nice book on quantum field theory in curved spacetime, with great analogy using driven harmonic oscillator and with many explicit examples. However, it only covers very limited aspects of the field as it focuses on examples; one needs to supplement this with other texts to be really useful. The appendices are very nice.

Quantum aspects of gravity

1. Gauge/Gravity Duality: Foundations and Applications (Martin Ammon, Johanna Erdmenger)
   Apart from numerous typos, very well-done text in trying to make a difficult subject more accessible to beginning researchers/graduate students. Used this for a reading course.

2. A First Course in String Theory (Barton Zwiebach)
   Very nice introduction to string theory (mostly not with Polyakov action), readable for advanced undergraduates. Found it useful as complement to Erdmenger/Ammon's string chapter.

3. Lecture Notes on Infrared Structure of Gravity and Gauge Theory (Andrew Strominger)
   Very recent book on new relationships between memory effect, asymptotic symmetry of spacetime and soft theorems. Hard to read without proper background, contrary to the book's claim but otherwise quite instructive.

Quantum information theory

1. Quantum Computation and Quantum Information (Michael A. Nielsen, Isaac L. Chuang)
   Standard reference in quantum information (including graduate course on the subject). It covers broad range of topics and gives enough details to appreciate the basic idea of each subject matter. Chapter 2 can even be treated as a condensed, crash course on quantum mechanics "without wavefunctions".

2. Theory of Quantum Computation (John Watrous)
   Very rigorous. Probably second book to go to after Nielsen/Chuang, and covers a lot of advanced tools that Nielsen/Chuang does not cover, such as Choi isomorphisms, semi-definite programming, unital channels, etc.

3. From Classical to Quantum Shannon Theory (Mark Wilde)
   Very nice lecture notes/book on quantum information and Shannon theory. It is of similar rigour as Watrous' book but with very different focus. Very nice reading if you have taken a course on quantum information or exposed to Nielsen/Chuang-level book.

Geometry and Topology

1. Topology and Geometry for Physicists (Charles Nash, Siddhartha Sen)
   Very small book attempting to introduce difficult concepts. Personally I find this to be very nice, complementary effort to Nakahara's similar, more complete text.

2. Geometry, Topology, and Physics (Mikio Nakahara)
   I find this to be a more comprehensive and detailed version of Nash/Sen, a highly recommended text that is even used in some pure mathematics courses (such as gauge theory that I took in University of Waterloo's special topics course).

3. An Introduction to Manifolds (Loring W. Tu)
   Very nice introduction, a good complement/substitute to the more well-known John Lee's texts.

4. An Introduction to Smooth Manifolds (John M. Lee)
   Standard book on the subject (I think), I like it as well as Tu's text.

5. Introduction to Riemannian Manifolds (John M. Lee)
   Standard book on the subject (I think?).

6. Lectures on Symplectic Geometry (Ana Cannas da Silva)
   Very nice, accessible introduction to symplectic manifolds, covering broad range of topics such as compatible triples, coadjoint orbits and moment maps.

Linear algebra & Lie algebra

1. Introduction to Lie Algebras (Karin Erdmann, Mark J. Wildon)
   Also with quite a number of typos, but they have comprehensive errata and very accessible, non-geometric version of Lie algebra introduction.

2. Linear Algebra Done Right (Sheldon Axler)
   My favourite textbook, which dispenses the whole use of determinant and trace till the very end, making a lot of proofs cleaner than standard methods. If you have read or learnt stuff in Friedberg's Linear Algebra, this will be a very good next book to read/skim.

Mathematical Methods

1. Complex Variables and Applications (James Ward Brown, Ruel V Churchill)
   Useful and explicit introduction to complex analysis techniques.

2. Fourier Analysis Generalized Functions (M. J. Lighthill)
   Very short but rigorous and accessible description of generalized function and Fourier analysis.