We describe how the CMB anisotropies are imprinted during and after recombination. First we develop the Sachs–Wolfe formula, based on the instantaneous recombination approximation, discussing the different terms (intrinsic, Doppler, gravitational redshift, and integrated Sachs–Wolfe). The description of polarization in terms of Stokes parameters and Jones and Mueller matrices is developed. The polarization dependence of Thomson scattering and its consequences are discussed. The phase space density evolution equations for photons, massless neutrinos, and also massive neutrinos are derived and the Boltzmann hierarchy for both the pure scalar and pure tensor sectors is derived. Using this formulation, the CMB anisotropy angular power spectra in temperature and in polarization are derived for both the pure scalar and pure tensor sectors. Reionization is discussed and also its impact on the polarization anisotropies at low multipole number. The practical numerical computation of the predicted CMB anisotropies are discussed and the predictions of the six-parameter concordance model are presented together with a qualitative interpretation.