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.