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A First Course in General Relativity by Bernard F. Schutz

This is a good book for students or self-learners who are at the advanced calculus level of math skills and want to move up gently to differential geometry and relativity. Schutz is very good at describing differential geometry in understandable physical language. This book makes the power of general relativity accessible to non-physicists, which is good, because why should we have all the fun?

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity by Steven Weinberg

This is the book that ended my mechnical engineering education. Forget heat transfer and thermal power systems, there is nothing as thrilling as the thermodynamics of an expanding universe. Weinberg teaches the elegant math of differential geometry from a physicist's perpective, which is a polite way to describe it. But what it lacks in mathematical elegance, the book more than makes up in the physical details and concrete calculations of stellar evolution, black hole formation, early universe expansion and gravitational radiation. This book is an absolute treasure if you want to learn how to get from the math to the measureable physical properties of the universe predicted by Einstein's theory.

The Nature of Space and Time (Isaac Newton Institute Series of Lectures) by Stephen Hawking, Roger Penrose (Contributor)

Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? On this issue, two of the world's most famous physicists disagree. Here, Stephen Hawking and Roger Penrose explain their positions in a work based on six lectures with a final debate, all originally presented at the Issac Newton Institute for Mathematical Sciences at the University of Cambridge.

Gravitation by Charles W. Misner, John Archibald Wheeler (Contributor), Kip S. Thorne (Contributor)

I think this is the biggest physics book ever printed in history. But that's because it has everything one could possibly teach a graduate student in physics about special and general relativity, plus, in a less difficult track in the book, everything one could possibly teach an undergraduate student in physics about special and general relativity. So it's like two relativity textbooks in one.

General Relativity by Robert M. Wald

Wald's book is suitable for graduate or advanced undergraduate students in physics who are comfortable with vectors, advanced calculus and geometry. This is a much more mathematical and much less physical treatment than given by Weinberg, and more compact and disciplined than the work by Misner, Thorne and Wheeler. Wald includes advanced topics such as causality, spacetime singularities, black hole thermodynamics, Hawking radiation and quantum field theory in curved spacetime.

General Relativity: A Geometric Approach by Malcolm Ludvigsen

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be presented in its simplest and most elegant form.

The Large Scale Structure of Space-Time by Stephen Hawking, G. F. Ellis (Contributor)

This has to be the most difficult book in all of theoretical physics. This is not a book for those just learning general relativity but it is irreplaceable for studying the most confounding and potentially problematic aspects of the theory, like singularities and violations of causality. If this book were a mountain, it would be a very steep and jagged one with a spectacular view at the top.

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