this volume contains papers presented at the meeting deformation theory, symplectic geometry and applications, held in ascona, june 17-21, 1996. the contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. new and important developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (ncg) and lie theory are presented. among the subjects treated are: quantization of general poisson manifolds; new deformations needed for the quantization of nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy lie algebras; finite- and infinite-dimensional lie groups; and 2d field theories and applications of ncg to gravity coupled with the standard model. audience: this book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and lie algebras.