I am looking to study cosmology at graduate level. Does any one recommend any introductory and comprehensive books for cosmology principles? I am interested in the maths too but I really want a book that introduces the principles and concepts first, to then dig deeper with the maths later.
39388
I have finished Carroll's general relativity book, Spacetime and Geometry. I am specifically interested in cosmology, so is there any book which goes more in depth into cosmology? I prefer a mathematically rigorous book, which goes beyond the cosmology chapter in Carroll's book. The Big Bang and inflation theory should be dealt with in depth.
58446
I want to learn some advanced topics in GR, such as . However nearly no textbooks on GR contain this area, such as Wald, MTW, Hawking, Carroll and  Zee's. Can anyone recommend some textbooks or papers giving the elaboration in detail?
52468
I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory course in real analysis but no other higher math.
37174
What is a good PDE book suitable for self study?   I'm looking for a book that doesn't require much prerequisite knowledge beyond undergraduate-level analysis.  My goal is to understand basic solutions techniques as well as some basic theory.
110094
I am almost finishing Gilbert Strang's book "An introduction to linear algebra" (plus video lectures at MIT OCW). First and foremost, I would like to suggest this course for everyone. It has been incredibly illuminating.   I would like to continue studying linear algebra, with particular focus on different properties of matrices and the transition to more general linear spaces (I am a physicist so Hilbert spaces and etc. are of particular interest).   Does anyone have a a good recommendation of books/resources/etc.?
70496
What is a good textbook on statistical field theory,  with an emphasis on applications to non-equilibrium phenomena?  I am a final-year undergraduate, have already taken introductory classes in statistical physics and quantum mechanics but do not know a lot of quantum field theory yet. I would like to better understand nonequilibrium phenomena, phase transitions and spontaneous symmetry breaking in condensed matter systems.
38124
I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
50994
Which books would you recommend, for self-studying homological algebra, to a beginning graduate (or advanced undergraduate) student who has background in ring theory, modules, basic commutative algebra (some of Atiyah &amp; Macdonald's book) and some (basic) field theory?  I would especially like to hear your opinions on the following books:  A Course On Homological Algebra / P. J Hilton and U. Stambach  Introduction to Homological Algebra / Szen-Tsen Hu  Notes on Homological Algebra / Rotman  But other recommendations will also be appreciated.
46068
I am looking for a book (English only) that I can treat as a reference text (more colloquially as a bible) about probability and is as complete - with respect to an undergraduate/graduate education in Mathematics - as possible. What I mean by that is that the book should contain and rigorously address the following topics:   Measure Theory (As a mathematical foundation for probability)   It is of course fine if this theory is addressed with an emphasis on probability and not only for the sake of mathematical measure theory, although the latter would be great too.  Introduction to Probability, i.e. the most common theory a student is exposed to when taking a first course in theoretic Probability. For example: distributions, expected value, modes of convergence, Borel Cantelli Lemmas, LLN, CLT, Gaussian Random Vectors More advanced topics such as: Conditional Expectation (defined through sigma-Algebras), Martingales, Markov Processes, Brownian Motion   I want it to be one book so I can carry a physical copy of it with me and work through the material in my spare time.   Examples:   The book by Jean-Francois Le Gall which can be found here:  but (unfortunately for me) is written in French.  Rick Durrett's book on Probability which can be found here  - the  for this book seems a bit mixed, uncertain about how to weigh that.   I am well aware that it's not easy to meet all of the above criteria simultaneously, but I would be grateful for any recommendation.
13552
I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth?
112904
I finished Introduction to Manifold by Loring Tu and I am interested to study this book by Milnor. But I didn't take a course in topology (other than the one I learnt from the appendix of Tu's book). Is this sufficient for me to read the book by Milnor?
60921
I'm curious to whether you guys have any tips on book concerning classical euclidean geometry. I'd like somewhat of an advanced treatment, around the same level as Coxeter's "Geometry revisited". I'd however want something more comprehensive, therefore I'm asking you for tips!  Hopeful for answers ^^
64259
There are no book recommendations for Astrophysics here. I will write my own answer, but I am also interested in what are others' views on the question (I will NOT mark my own answer as the best one).
115450
I have recently been reading Intro to Lie algebras and representation theory by Humphreys, and when I am finished I am interested in reading about Lie groups and Lie algebras and their applications to particle physics.     Is there a book that assumes basic knowledge of Lie algebras, and no knowledge of lie groups and particle physics/quantum mechanics?   I have seen Howard Georgi's book, but it assumes good knowledge of particle physics.   In addition, I do not know differential geometry.
79938
I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic Analysis, but perhaps I must first study the foundations of quantum mechanics. So I would like to know what book you recommend me to begin studying quantum mechanics. I'm primarily interested in a mathematical point of view. I have seen some books of this type, but I would like to have some other opinion.  Thanks for every reply
11241
What is your recommendation for an in-depth introductory combinatoric book? A book that doesn't just tell you about the multiplication principle, but rather shows the whole logic behind the questions with full proofs. The book should be for a first-year-student in college. Do you know a good book on the subject?  Thanks.
2223
I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course, it's always good to give as much intuition about the material.  Some things I'd be happy if it includes (but again, it mostly just needs to be a clear book even if it doesn't contain these) are:   As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates. Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas.