ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Contents: Volume II: The Proper Forcing Axiom (J T Moore); Tensor Triangular Geometry (P Balmer); The Emerging p-adic Langlands Programme (C Breuil); The Tangent Space to an Enumerative Problem (P Belkale); Scalar Curvature, Conformal Geometry, and the Ricci Flow with Surgery (F C Marques); Fukaya Categories and Bordered Heegaard-Floer Homology (D Auroux); Volume III: Quasi-isometric Rigidity of Solvable Groups (A Eskin & D Fisher); Differentiability of Lipschitz Functions, Structure of Null Sets, and Other Problems(M Csrnyei et al.); Group Actions on Operator Algebras (M Izumi); Green Bundles and Related Topics (M-C Arnaud); A Hyperbolic Dispersion Estimate, with Applications to the Linear Schrdinger Equation (N Anantharaman et al.); Topological Field Theory, Higher Categories, and Their Applications (A Kapustin); Volume IV: Random Planar Metrics (I Benjamini); Flag Enumeration in Polytopes, Eulerian Partially Ordered Sets and Coxeter Groups (L J Billera); Smoothed Analysis of Condition Numbers (P Brgisser); The Hybridizable Discontinuous Galerkin Methods (B Cockburn); Optimal Control under State Constraints (H Frankowska); Deterministic and Stochastic Aspects of Single-crossover Recombination (E Baake); Professional Knowledge Matters in Mathematics Teaching (J Adler); History of Convexity and Mathematical Programming: Connections and Relationships in Two Episodes of Research in Pure and Applied Mathematics of the 20th Century (T H Kjeldsen); and other papers.