  These lecture notes treat the mean-field approximation for equilibrium states
of N body systems in classical and quantum statistical mechanics. A general
strategy to justify effective models based on assumptions of statistical
independence of the particles is in presented in detail. The main tools are a
structure theorems of de Finetti that describe large N limits of states
accessible to the systems in question, exploiting the indistinguishablity of
particles. The focus is on quantum aspects, particularly the mean-field
approximation for the ground state of a large system of bosons, in connection
with Bose-Einstein condensation: structure of reduced density matrices of a
large bosonic system, localization methods in Fock space, derivation of Hartree
and non-linear Schr\"odinger effective energy functionals.
