The papers in this volume are based on lectures given during the meeting of the Seminaire Sud Rhodanien de Geometrie which we organized at MSRI from May 22 to June 2, 1989, as part of a year-long program on Symplectic Geometry and Mechanics. The Seminaire Sud Rhodanien de Geometrie (SSRG) was established in 1982 by geometers and mathematical physicists at the Universities of Avignon, Lyon, Marseille, and Montpellier, with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. It has been designated by the Centre N ationale de la Recherche Scientifique as a "Groupement de Recherche" (G.D.R. 144), centered at the Universite Claude Bernard (Lyon I). From the beginning, the SSRG has involved the cooperation of colleagues from other universities inside and outside France; in addition to the editors of this volume, its Scientific Committee consists of D. Bennequin, P. Libermann, A. Lichnerowicz, C.-M. MarIe, J.-M. Morvan, P. Molino, and J.-M. Souriau. In particular, there have always been strong connections with the University of California at Berkeley, making this other "UCB" into a virtual fifth pole of the SSRG. Through its international meetings, of which the first five were held at Lyon, Montpellier, and Marseille, the SSRG has become an important cen­ ter of exchange for the latest developments in symplectic geometry and its applications. It seemed natural, therefore, to have this sixth meeting at MSRI in Berkeley in conjunction with the "symplectic year" 1988-89.

Groupoïdes de Lie et Groupoïdes Symplectiques.- Géométrie Globale des Systèmes Hamiltoniens complètement Intégrables et Variables Action-Angle avec Singularités.- Sur Quelques Questions de Géométrie Symplectique.- Intégration Symplectique Des Variétés de Poisson Totalement Asphériques.- La Première Classe de Chern Comme Obstruction à la Quantification Asymptotique.- Groupes de Poisson Affines.- Singular Lagrangian Foliation Associated to An Integrable Hamiltonian Vector Field.- Hyperbolic Actions of Rp on Poisson Manifolds.- Compactification D'actions de ?n et Variables Action-Angle avec Singularités.- On the Diameter of the Symplectomorphism Group of the Ball.- A Symplectic Analogue of the Mostow-Palais Theorem.- Melnikov Formulas for Nearly Integrable Hamiltonian Systems.- A Non-Linear Hadamard Theorem.- Equivariant Prequantization.- Momentum Mappings and Reduction of Poisson Actions.- On Jacobi Manifolds and Jacobi Bundles.- Groupes de Lie à Structure Symplectique Invariante.- Holonomy Groupoids of Generalized Foliations. II. Transverse Measures and Modular Classes.- Symplectic Groupoids, Geometric Quantization and Irrational Rotation Algebras.- Morita Equivalent Symplectic Groupoids.