Space - Time - Matter
by Hermann Weyl
Publisher: Methuen & Co. 1922
Number of pages: 517
A classic of physics -- the first systematic presentation of Einstein's theory of relativity. Long one of the standard texts in the field, this excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation.
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by Edward Witten - arXiv.org
This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem.
by Edmund Bertschinger - MIT
Working with GR requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
by V. L. Kalashnikov - arXiv
The author presents the pedagogical introduction to relativistic astrophysics and cosmology, which is based on computational and graphical resources of Maple 6. The knowledge of basics of general relativity and differential geometry is supposed.
by Sean M. Carroll
General relativity has a reputation of being extremely difficult. This introduction is a very pragmatic affair, intended to give you some immediate feel for the language of GR. It does not substitute for a deep understanding -- that takes more work.