Quasiconformal mappings, Teichmüller spaces, and Kleinian groups / Calcul infinitesimal stochastique / On Kähler varieties of restricted type / Rational approximations to algebraic numbers / Autobiography / Looking forward from ICM 1962 / The index of elliptic operators / A survey of some recent developments in differential topology / Effective methods in the theory of numbers ; Effective methods in Diophantine problems -- Effective methods in Diophantine problems. II -- Effective methods in the theory of numbers/Diophantine problems / Rôle of integrable models in the development of mathematics / Pattern theory: a unifying perspective / Oppenheim conjecture / Brisure de symétrie spontanée et géométrie du point de vue spectral / Remarks on gauge theory, complex geometry and 4-manifold topology / Betti number estimates for nilpotent groups / A polynomial invariant for knots via von Neumann algebras -- Index for subfactors / Birational classification of algebraic threefolds / Geometry and quantum field theory / Hamiltonian methods in nonlinear evolution equations / On some recent mthods for nonlinear partial differential equations / Recent developments in dynamics / On the restricted Burnside problem / What is moonshine? / A new proof of Szemeredi's theorem for arithmetic progressions of length four / Formal (non)-commutatuve symplectic geometry ; Comments on "Formal (non)-commutative symplectic geometry" / Rigidity and inflexibility in conformal dynamics / Open problems in the motivic style homotopy theory, I