  We present a formalism for analyzing a full-sky temperature and polarization
map of the cosmic microwave background. Temperature maps are analyzed by
expanding over the set of spherical harmonics to give multipole moments of the
two-point correlation function. Polarization, which is described by a
second-rank tensor, can be treated analogously by expanding in the appropriate
tensor spherical harmonics. We provide expressions for the complete set of
temperature and polarization multipole moments for scalar and tensor metric
perturbations. Four sets of multipole moments completely describe isotropic
temperature and polarization correlations; for scalar metric perturbations one
set is identically zero, giving the possibility of a clean determination of the
vector and tensor contributions. The variance with which the multipole moments
can be measured in idealized experiments is evaluated, including the effects of
detector noise, sky coverage, and beam width. Finally, we construct
coordinate-independent polarization two-point correlation functions, express
them in terms of the multipole moments, and derive small-angle limits.
