Spacetime and Geometry

Spacetime and Geometry: An Introduction to General Relativity is a textbook written by physicist Sean Michael Carroll for beginning graduate students in physics. The book was developed from the lecture notes for a graduate course on general relativity Carroll taught at the Massachusetts Institute of Technology. Compared to the lecture notes, still available online for free from Carroll's personal website, the book is newer and contains more worked examples.

Spacetime and Geometry occupies the middle ground between a rigorous mathematical presentation and a utilitarian approach. Like many other textbooks, it develops the necessary mathematical concepts in differential geometry—especially covariant differentiation and the curvature tensor—before exploring its main subject matter. It covers the standards topics in general relativity. But unlike other introductory texts, it includes a chapter on quantum field theory in flat as well as curved spacetime. Its discussion of cosmology, a rapidly growing field, is up-to-date for its time, with an account of inflation.