A partition of a positive integer n is a non-increasing sequence of numbers whose sum is n, the partitions of 3 being (3), (2,1) and (1,1,1). Though simple to define, these objects are very deep combinatorially. The goal of this course is to present different aspects of the theory of integer partitions (mostly combinatorial, but also number theoretic and algebraic): generating functions, partition identities, congruences, asymptotics...