Lecture Notes on General Relativity
arXiv:gr-qc/9712019
Abstract
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.
238 pages, numerous figures. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/notes/