  These notes deal with the mean-field approximation for equilibrium states of
N-body systems in classical and quantum statistical mechanics. A general
strategy for the justification of effective models based on statistical
independence assumptions is presented in details. The main tools are structure
theorems {\`a} la de Finetti, describing the large N limits of admissible
states for these systems. These rely on the symmetry under exchange of
particles, due to their indiscernability. Emphasis is put on quantum aspects,
in particular the mean-field approximation for the ground states of large
bosonic systems, in relation with the Bose-Einstein condensation phenomenon.
Topics covered in details include: the structure of reduced density matrices
for large bosonic systems, Fock-space localization methods, derivation of
effective energy functionals of Hartree or non-linear Schr{\"o}dinger type,
starting from the many-body Schr{\"o}dinger Hamiltonian.
