  This review presents, in a self-consistent manner, those analytical tools
that are relevant for the analysis of the physics of CMB anisotropies generated
in different theoretical models of the early Universe. After introducing the
physical foundations of the Sachs-Wolfe effect, the origin and evolution of the
scalar, tensor and vector modes of the geometry is treated in both
gauge-invariant and gauge-dependent descriptions. Some of the recent progresses
in the theory of cosmological perturbations are scrutinized with particular
attention to their implications for the adiabatic and isocurvature paradigms,
whose description is reviewed both within conventional fluid approaches and
within the the Einstein-Boltzmann treatment. Open problems and theoretical
challenges for a unified theory of the early Universe are outlined in light of
their implications for the generation of large-scale anisotropies in the CMB
sky and in light of the generation of stochastic backgrounds of relic gravitons
between few Hz and the GHz.
