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Have you had a look at Carroll's general relativity notes? Chapters 2 and 3 are predominantly about developing the mathematics behind GR, and are very good introductions to this. I have a copy of Carroll's book and I can promise you that those chapters are almost unchanged in the book as compared to the lecture notes. This is my main suggestion really, as the notes are freely available, written by an absolute expert and a joy to read. I can't recommend them (and the book really) enough.

Most undergraduate books on general relativity start with a "physics first" type approach, where the underlying material about manifolds and curvature is developed as it is needed. The only problem with this is that it makes seeing the underlying picture for how the material works more difficult. I wouldn't neccessarily say avoid these sort of books (my favourite two of this kind would be Cheng's book and Hartle's.) but be aware that they are probably not what you are looking for if you want a consistent description of the mathematics.

I would also say avoid the harder end of the scale (Wald) till you've at least done your course. Wald is a tough book, and certainly not aimed at people seeing the material for the first time.

Another useful idea would be looking for lecture notes from other universities. As an example, there are some useful notes here from cambridge university. Generally I find doing searches like "general relativity site:.ac.uk filetype:pdf" in google is a good way to get started searching for decent lecture notes from other universities.

If you're willing to dive in a bit more to the mathematics, the riemannian geometry book by DoCarmo is supposed to be excellent, although I've only seen his differential geometry book (which was very good). As a word of warning, this book might assume knowledge of differential geometry from his earlier book. The book you linked by Bishop also looks fine, and there is also the book by Schutz which is supposed to be great and this book by Sternberg which looks pretty good, although quite tough.

Finally, if you would like I have a dropbox folder of collected together material for GR which I could share with you. It's not much, but I've got some decent stuff collected together which could be very helpful. As a qualifier, I had to teach myself GR for my undergrad project, so I know how it feels being on your own with it. Good luck!

No; I haven't read it or anything else by Linus Pauling. Have a read and see if it's right for you - that edition is probably going to be more or less the same as (if not identical to) the Dover print.

It looks like a good general introduction to quantum mechanics, and would likely be a good extracurricular read if not for a course. If you're a student in need of a more comprehensive text, I'd probably recommend something slightly more recent and thorough - Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles by Eisberg and Resnick is a great book for that. You could get both, read Pauling's text and then turn to Eisberg and Resnick when you feel Pauling hasn't gone into enough detail or explained something very well.

Ah - I've just seen your earlier post. In which case, the Pauling book would be fine. Again, though, have a scan through the pdf above (in particular, the contents) and make sure it's what you expect/want to read. It might be a little dry. A good in-between might be The Principles of Quantum Mechanics by Paul Dirac, a very recommended text that is comprehensive without being laboriously dull (as far as I've heard). Again, a pdf to peruse can be found here - judge for yourself!

I agree with rnally that in order to really get a hold of General Relatively you will need to know differential geometry (which in itself requires you to know calculus and differential forms, multivariable calculus, linear algebra, and maybe a bit of tensor analysis). However don't be discouraged, with just high school math you should be able to figure our Special Relativity. It brings me back memories of when I was a high school senior trying to figure out relativity myself and read Relativity: The Special and the General Theory by Albert Einstein. It's a neat little book and you should be able to get through the first half on special relativity (the highest math I saw were square roots), but again don't be discouraged when you hit the section on general relativity and if you understand everything up to that point you would have gone farther than I have when I was your age :). Best of luck! and good choice of major! (Majored in physics myself)

If you want to start with mechanics, Spivak of all people [wrote a mechanics text.] (http://www.amazon.com/gp/aw/d/0914098322) I've personally never read it, but I've suffered more than enough at his hands read enough of his other works to expect good things.

In more advanced physics, there's general relativity, which is built on manifold theory, and gauge theory, which has lots of interesting math happening behind the scenes (and sometimes very prevalently, as with the gauge groups, usually taken to be SU(n)). Most physics texts will treat the mathier topics as of secondary interest and importance, and focus on the actual physics, so you might have some trouble finding an appropriately rigorous text, but there certainly exist such entities.

This may be a bit too advanced than what you are looking for and less of a historical text but it is a definitive and a text written by Maxwell on how Electromagnetism came about. It is very much a good text to accompany texts like Jackson and very advanced E&M since it goes through the thoughts and the motivation that Maxwell had when finishing up the Maxwell Equations. They are very thick and detailed and not light reading at all but I thought maybe I should add these here since they describe the thought process of Maxwell.

Book 1

Book 2

I think most have provided the standard intro to GR textbooks at this point, so I'll make a vote here for Flat and Curved Spacetimes by Ellis and Williams. The illustrations, examples, and exercises in there are quite enlightening for one encountering SR and GR for the first time. Also, the annotated bibliography at the end of each chapter is an excellent resource to guide one to more advanced reading.

I didn't like the Kittel book, and we used this Steve Simon book for my solid state course at Uni.
It's one of the funniest textbooks I've ever had, actually. Lots of little comedic asides.

However, he also has basically the whole book on his website for free anyway (with some errors that are resolved in the printed version)

I know this isn't exactly what you wanted, but Gravitation by Misner, Wheeler and Thorne ranks among mankind's most brilliant scientific achievements. This book is a tour-de-force of GR, with deep insights in every chapter, though some parts are a little out of date. You may be able to get a used copy for cheap.

You can get an eTextbook version from Pearson at http://www.mypearsonstore.com/bookstore/mechnics-of-materials-coursesmart-etextbook-0133254690 , or a physical copy either from Pearson or Amazon (http://www.amazon.com/Mechanics-Materials-Edition-Russell-Hibbeler/dp/0133254429). If you want a free copy, check your library.

I can't speak from personal experience since I haven't started working on the book yet but this is a question I've asked before too and from googling I saw many recommendations for G.K. Batchelor: http://rads.stackoverflow.com/amzn/click/0521663962

"An Introduction to Fluid Dynamics" by G. K. Batchelor is a classic and is considered as the Bhagavad Gita of fluid dynamics. I have read this book as an undergrad and hence the knowledge required is just high school mathematics and physics.