Description:A note to readers: This book is in French. This 65th volume of the Bourbaki Seminar contains the texts of the fifteen survey lectures presented during 2012/2013 on the following topics: Hodge theory; the structure of certain homeomorphism groups of a Cantor space; differential equations in metric spaces; stochastic partial differential equations; probability theory; laminations and 3-dimensional manifolds; finite groups; the representations of classical groups and on the categorification of those of Lie algebras; the Bloch-Kato conjecture in Galois cohomology; algebraic geometry; ergodic theory; the hyperbolicity of hypersurfaces in projective spaces; the Baum-Connes conjecture.