The five lectures presented in this volume address very timely mathematical problems in relativity and cosmology. Part I is devoted to the initial value and evolution problems of the Einstein equations. Especially it deals with the Einstein-Yang-Mills-Boltzmann system, fluid models with finite or infinite conductivity, global evolution of a new (two-phase) model for gravitational collapse and the structure of maximal, asymptotically flat, vacuum solutions of the constraint equations which have the additional property of containing trapped surfaces. Part II focuses on geometrical-topological problems in relativity and cosmology: on the role of cosmic censorship for the global structure of the Einstein-Maxwell equations and on the mathematical structure of quantum conformal superspace.
From the contents: Part I. Initial Value and Evolution Problems:- Yang-Mills Plasmas.- Relativistic Fluids and Gravitational Collapse.- The Einstein Vacuum Constraints and Trapped Surfaces. Part II. Global Structures:- Black Hole Collisions, Analytic Continuation and Cosmic Censorship.- The Structure of Quantum Conformal Superspace.