The purpose of this volume is to present new techniques and ideas that have a di­ rect significance for the description of stratified (symplectic) spaces and their quan­ tization. The book grew out of a Research-in-Pairs Workshop held at Oberwolfach from 2-6 August, 1999, organized by the editors with Martin Bordemann. They are grateful to the Volkswagen-Stiftung and to the Mathematisches Forschungszen­ trum Oberwolfach, particularly to its director, Matthias Kreck, for financial and other support. The papers by Cattaneo and Felder, Huebschmann, Landsman, Pflaum, Schli­ chenmaier, Schomerus, Schroers, and Sengupta are based on talks given at the workshop. To obtain a more complete picture of the field, the editors invited a number of outside contributions as well. Thus they are happy to include the papers by Benameur and Nistor, Braverman, Fedosov, and Lauter and Nistor. All papers were refereed. The opening article by Marsden and Weinstein provides a historical and personal overview of the subject. In the bulk of the book the reader may identify two fundamentally different approaches. The first associates a commutative algebra of functions to a singular space, preferably also equipped with a Poisson bracket, which one may subse­ quently try to quantize. This generically involves techniques from algebraic and differential geometry. Here the papers by Braverman, Cattaneo and Felder, Pflaum, and Schlichenmaier are of a general nature, whereas Huebschmann, Schomerus, Schroers, and Sengupta are specifically concerned with the moduli spaces M. (Cf.