  These lecture notes present the computation of the full system of Boltzmann
equations describing the evolution of the photon, baryon and cold dark matter
fluids up to second order in perturbation theory, as recently studied in
(Bartolo, Matarrese & Riotto 2006, 2007). These equations allow to follow the
time evolution of the cosmic microwave background anisotropies at all angular
scales from the early epoch, when the cosmological perturbations were
generated, to the present, through the recombination era. The inclusion of
second-order contributions is mandatory when one is interested in studying
possible deviations from Gaussianity of cosmological perturbations, either of
primordial (e.g. inflationary) origin or due to their subsequent evolution.
Most of the emphasis in these lectures notes will be given to the derivation of
the relevant equations for the study of cosmic microwave background
anisotropies and to their analytical solutions.
