Proceedings of the workshop held in Estérel, Quebec, May 22--29, 1994. Edited by Decio Levi, Luc Vinet and Pavel Winternitz. CRM Proceedings & Lecture Notes, 9.

Contents: M. J. Ablowitz, B. M. Herbst and C. Schober, On the numerics of integrable discretizations (1--11); Richard Askey, A brief introduction to the world of $q$ (13--20); Natig M. Atakishiyev [N. M. Atakishiev], A Ramanujan-type measure for the Al-Salam and Ismail biorthogonal rational functions (21--27); H. M. Babujian [G. M. Babudzhyan] and R. Flume, Knizhnik-Zamolodchikov equations and the algebraic Bethe ansatz (29--35); H. W. Capel and F. W. Nijhoff, Integrable quantum mappings (37--49); Igor Cherdantsev [I. Yu. Cherdantsev] and Ravil Yamilov [R. I. Yamilov], Local master symmetries of differential-difference equations (51--61); Peter A. Clarkson and Andrew P. Bassom, Backlund transformations and hierarchies of exact solutions for the fourth Painleve equation and their application to discrete equations (63--77); J. F. van Diejen, On the diagonalization of difference Calogero-Sutherland systems (79--89); Adam Doliwa and Paolo Maria Santini, The integrable dynamics of a discrete curve (91--102); Vladimir Dorodnitsyn [V. A. Dorodnitsyn], Continuous symmetries of finite-difference evolution equations and grids (103--112); Roberto Floreanini and Luc Vinet, Basic Bessel functions and $q$-difference equations (113--123); D. V. Fursaev and V. G. Kadyshevsky [V. G. Kadyshevskii], Difference equations and gauge symmetry (125--132).

Holger Frahm, Alexander R. Its [A. R. Its] and Vladimir E. Korepin [V. E. Korepin], An operator-valued Riemann-Hilbert problem associated with the XXX model (133--142); F. Alberto Grunbaum and Luc Haine, Orthogonal polynomials satisfying differential equations: the role of the Darboux transformation (143--154); J. Harnad, Quantum isomonodromic deformations and the Knizhnik-Zamolodchikov equations (155--161); Nalini Joshi and Peter J. Vassiliou, Lie symmetries and linearizations of analytic discrete dynamical systems (163--171); E. G. Kalnins and Willard Miller, Jr., $q$-algebra representations of the Euclidean, pseudo-Euclidean and oscillator algebras, and their tensor products (173--183); Vadim B. Kuznetsov [V. B. Kuznetsov], $\sb 3F\sb 2(1)$ hypergeometric function and quadratic $R$-matrix algebra (185--197); Decio Levi and Pavel Winternitz, Lie point symmetries of differential-difference equations (199--208); R. M. Mir-Kasimov, The factorization method for the differential-difference relativistic Schrodinger equation and $q$-deformations (209--218); A. Mironov [A. D. Mironov], Quantum deformations of $\tau$-functions, bilinear identities and representation theory (219--237); Javier Negro, The factorization method and hierarchies of $q$-oscillator Hamiltonians (239--251); F. W. Nijhoff and G. D. Pang [Gen Di Pang], Discrete-time Calogero-Moser model and lattice KP equations (253--264); Yasuhiro Ohta, Kenji Kajiwara and Junkichi Satsuma, Bilinear structure and exact solutions of the discrete Painleve I equation (265--268).

V. Papageorgiou, B. Grammaticos and A. Ramani, Integrable difference equations and numerical analysis algorithms (269--280); Mizan Rahman, An integral representation of the very-well-poised $\sb 8\psi\sb 8$ series (281--287); Mizan Rahman and Sergei K. Suslov [S. K. Suslov], Singular analogue of the Fourier transformation for the Askey-Wilson polynomials (289--302); A. Ramani, B. Grammaticos and V. Papageorgiou, Singularity confinement (303--318); A. Ronveaux, S. Belmehdi, E. Godoy and A. Zarzo, Recurrence relation approach for connection coefficients. Applications to classical discrete orthogonal polynomials (319--335); R. Sahadevan, G. B. Byrnes and G. R. W. Quispel, Linearisation of difference equations using factorisable Lie symmetries (337--343); A. B. Shabat, First integrals of the infinite Toda lattice (345--351); E. Sorace, Non-semisimple quantum groups and "exponential mappings" (353--362); Vyacheslav Spiridonov [V. P. Spiridonov], Luc Vinet and Alexei Zhedanov [A. S. Zhedanov], Discrete Schrodinger equation, Darboux transformations, and orthogonal polynomials (363--369); Leon A. Takhtajan, Integrable cellular automata and AKNS hierarchy (371--375); Claude M. Viallet, On some rational Coxeter groups (377--388).

\{The papers are being reviewed individually.\}