Discrete integrable systems : [... contains ten courses based on the lectures delivered at the International School on Discrete Integrable Systems ... which was held in Pondicherry India from February 2 to February 14 2003] This volume consists of a set of ten lectures conceived as both introduction and up to date survey on discrete integrable systems. It constitutes a companion book to Integrability of Nonlinear Systems (Springer Verlag 2004 LNP 638 ISBN 3 540 20630 2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics. TOC:Three Lessons on the Painlevé Property and the Painlevé Equations. Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems. Special Solutions of Discrete Integrable Systems. Discrete Differential Geometry. Integrability as Consistency. Discrete Lagrangian Models. Symmetries of Discrete Systems. Discrete Painlevé Equations: a Review. Special Solutions for Discrete Painlevé Equations. Ultradiscrete Systems (Cellular Automata). Time in Science: Reversibility vs. Irreversibility