This book is written in a pedagogical style intelligible for graduate students. It reviews recent progress in black-hole and wormhole theory and in mathematical cosmology within the framework of Einstein's field equations and beyond, including quantum effects. This collection of essays, written by leading scientists of long standing reputation, should become an indispensable source for future research. TOC:Global Wave Maps on Curved Space Times.- Einstein's Equations and Equivalent Hyperbolic Dynamical Systems.- Generalized Bowen--York Initial Data.- The Reduced Hamiltonian of General Relativity and the "sigma"-Constant of Conformal Geometry.- Anti-de-Sitter Spacetime and Its Uses.- Black Holes and Wormholes in 2+1 Dimensions.- Open Inflation.- Generating Cosmological Solutions from Known Solutions.- Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-Branes.- Open Issues.