  This is the first of a series of papers extending a covariant and gauge
invariant (CGI) treatment of kinetic theory in curved space-times to a
treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising
from inhomogeneities in the early universe. This paper deals with algebraic
issues, both generically and in the context of models linearised about RW
geometries.
  The approach represents radiation anisotropies by PSTF tensors. The Angular
correlation functions for the mode coefficients are found in terms of these
quantities, following the Wilson-Silk approach, but derived and dealt with in
CGI form. The covariant multipole and mode-expanded angular correlation
functions are related to the usual treatments in the literature. The CGI mode
expansion is related to the coordinate approach by linking the Legendre
functions to the PSTF representation, using a covariant addition theorem for
the tensors to generate the Legendre Polynomial recursion relation.
  This paper lays the foundation for further papers in the series, which use
this formalism in a CGI approach to develop solutions of the Boltzmann and
Liouville equations for the CBR before and after decoupling, thus providing a
unified CGI derivation of the variety of approaches to CBR anisotropies in the
current literature.
