Right now, I’m taking a course on General Relativity with Justin Khoury here at Penn. As I work through the problem sets and supplement my lecture notes, I’ve compiled a list of what I think are the most useful books on the topic. I’m sure I’ll find more as the course goes on, but here are some that every fledgling physicist should own:
Weinberg’s Gravitation and Cosmology. This book is fantastic, which is not surprising since it’s written by the man who is arguably one of the greatest (if not the greatest) physicist alive. He walks the reader through Special Relativity, General Relativity, and Cosmology. My favorite aspect of the book is how solid his explanation of the math behind GR is, which is kind of a big deal given that the math is essential to understanding anything about GR. I reference it every day, even more frequently than Carroll’s book (which is listed below). One thing to be wary of: if you’ve ever picked up one of Weinberg’s books (whether it’s one of his famous – or infamous – books on quantum field theory or cosmology), it’s not really a book to learn from, but more of a reference to turn to whenever you need insights into various intricacies of GR.
Carroll’s Spacetime and Geometry. This is the book most often used in GR courses, and for good reason: Carroll’s explanations are fantastic. The only downside of the book is the fact that you can’t use it as your only textbook on the topic, because he does gloss over some important things. Think of this book as a set of detailed lecture notes: covers the necessary parts, and needs supplementation by other books (Weinberg, Wald, and all the cool lecture notes you can find online).
Wald’s General Relativity. Most of the theorists I know consider this the holy grail of general relativity texts. Wald covers things that I haven’t been able to find in any other books – these things are found in the second half of the book. (I especially like the section on spinor fields). If you’re theory bent, you should be hell-bent on truly understanding this book, and will find it to be in the spirit of Peskin and Schroeder (which is, for the book and its readers, a blessing and a curse – all you theory students will know exactly what I mean). Work out the problems.