Spacetime and geometry : - Carroll, Sean M. (Addison Wesley, 2004)
Carroll (University of Chicago) explains the mathematical strategy of describing gravity as the geometry of a curved manifold, derives Einstein's field equation for the metric in general relativity, and discusses the three major applications of general relativity: black holes, perturbation theory, and gravitational waves. This graduate textbook also provides a brief introduction to quantum field theory in curved spacetime.