The role of the geometry of manifolds in space-time physics, and that of functional analysis in quantum mechanics and quantum field theory have become increasingly important. This is particularly true in the study of the global behaviour of solutions of differential systems on manifolds, and their implications to general relativity. Yvonne Choquet-Bruhat has contributed much to this exciting area of mathematical physics, and her work on the existence of solutions to Einstein's equations on differential manifolds of a general type has subsequently stimulated and inspired much important research. She has also played a pioneering role in the study of global problems, especially in gauge field theory and supergravity, and in the development of a theory of asymptotic gravitational and electromagnetic waves. The various contributions appearing in this volume, authored by eminent scientists, illustrate the latest developments in the many areas of contemporary physics which have greatly benefited from Choquet-Bruhat's work and influence. For mathematical physicists with an interest in relativity, quantum mechanics and field theory.