This is a review of the theory of CMB anisotropies, an updated version of a course given at the troisieme cycle de la Suisse Romande. An introduction to gauge invariant cosmological perturbation theory is given and the theory CMB anisotropies is develiped in this context. Simple analytical approximations for the acoustic peak positions for adiabatic and isocurvature perturbations are derived. Silk damping is discussed by an analytic approximation. A short description of the present status of observations and parameter estimation followed by a critical discussion terminate the review. The full system of differential equations for CMB anisotropies and polarization needed in a numerical treatment is also developed and given in an appendix.