This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference in General Relativity, held in June 1986 at the University of California, Santa Cruz. General relativity is one of the most successful alliances of mathematics and physics. It provides us with a theory of gravity which agrees with all experimentation and observation to date. In addition, there is a great deal of physical evidence for a number of interesting effects predicted by the theory of gravity--black holes, cosmological expansion, gravitational waves, and gravitational lenses. The enabling tool is the language of differential geometry. Throughout its 70-year history, general relativity has significantly stimulated pseudo-Riemannian as well as Riemannian geometry and has also motivated important work in complex geometry, topology, and the study of both elliptic and hyperbolic systems of partial differential equations.