  This is a presentation of recent work on quantum permutation groups.
Contains: a short introduction to operator algebras and Hopf algebras; quantum
permutation groups, and their basic properties; diagrams, integration formulae,
asymptotic laws, matrix models; the hyperoctahedral quantum group, free wreath
products, quantum automorphism groups of finite graphs, graphs having no
quantum symmetry; complex Hadamard matrices, cocycle twists of the symmetric
group, quantum groups acting on 4 points; remarks and comments.
