This book presents a panorama of finite dimensional completely integrable Hamiltonian systems, in which classical aspects and quantum aspects will be living side by side, with similar appearances. Classical mechanics is considered from the viewpoint of the geometric study of the singular Lagrangian foliation, whose regular leaves are the famous Liouville tori. Singularities are tackled using local and semiglobal normal forms, which involve topological and symplectic invariants. Some relationships with toric varieties are explored. Quantum integrable systems are treated in the framework of semiclassical microlocal analysis. Pseudodifferential calculus and Fourier integral operators offer efficient tools for discovering how the geometric features of these systems influence their spectral properties. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in discrete mathematics and combinatorics. Table of Contents  Introduction
 Introduction à l'analyse semiclassique
 Exemples fondamentaux de systèmes intégrables
 Théorie locale
 Théorie semiglobale
 Théorie globale
 Bibliographie
 Liste des figures
 Index
