This book constitutes the proceedings of the International Conference on Integrable Systems in memory of J.-L. Verdier. It was held on July 1-5, 1991 at the Centre International de Recherches Mathematiques (C.I.R.M.) at Luminy, near Marseille (France). This collection of articles, covering many aspects of the theory of integrable Hamiltonian systems, both finite­ and infinite-dimensional, with an emphasis on the algebro-geometric meth­ ods, is published here as a tribute to Verdier who had planned this confer­ ence before his death in 1989 and whose active involvement with this topic brought integrable systems to the fore as a subject for active research in France. The death of Verdier and his wife on August 25, 1989, in a car accident near their country house, was a shock to all of us who were acquainted with them, and was very deeply felt in the mathematics community. We knew of no better way to honor Verdier's memory than to proceed with both the School on Integrable Systems at the C.I.M.P.A. (Centre International de Mathematiques Pures et Appliquees in Nice), and the Conference on the same theme that was to follow it, as he himself had planned them.

Hommage à Jean-Louis Verdier: au jardin des systèmes intégrables.- I. Algebro-Geometric Methods and ?-Functions.- Compactified Jacobians of Tangential Covers.- Heisenberg Action and Verlinde Formulas.- Hyperelliptic Curves that Generate Constant Mean Curvature Tori in ?3.- Modular Forms as ?-Functions for Certain Integrable Reductions of the Yang-Mills Equations.- The ?-Functions of the gAKNS Equations.- On Segal-Wilson's Definition of the ?-Function and Hierarchies AKNS-D and mcKP.- The Boundary of Isospectral Manifolds, Bäcklund Transforms and Regularization.- II. Hamiltonian Methods.- The Geometry of the Full Kostant-Toda Lattice.- Deformations of a Hamiltonian Action of a Compact Lie Group.- Linear-Quadratic Metrics "Approximate" any Nondegenerate, Integrable Riemannian Metric on the 2-Sphere and the 2-Torus.- Canonical Forms for Bihamiltonian Systems.- Bihamiltonian Manifolds and Sato's Equations.- III. Solvable Lattice Models.- Generalized Chiral Potts Models and Minimal Cyclic Representations of $${U_q}(\widehat{gl}(n,C))$$).- Infinite Discrete Symmetry Group for the Yang-Baxter Equations and their Higher Dimensional Generalizations.- IV. Topological Field Theory.- Integrable Systems and Classification of 2-Dimensional Topological Field Theories.- List of Participants.