The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevaninna, Gauss and Leelavati Prizes and the Chern Medal laudations. Contents: Logic and Foundations; Algebra; Number Theory; Algebraic and Complex Geometry; Geometry; Topology; Lie Theory and Generalizations; Analysis and Operator Algebras; Dynamical Systems and Ordinary Differential Equations; Partial Differential Equations; Mathematical Physics; Probability and Statistics; Combinatorics; Mathematical Aspects of Computer Science; Numerical Analysis and Scientific Computing; Control Theory and Optimization; Mathematics in Science and Technology; Mathematics Education and Popularization of Mathematics; History of Mathematics.