  We present here a detailed, self--contained treatment of the mathematical
formalism for describing the theory of polarized anisotropy in the cosmic
microwave background. This didactic review is aimed at researchers who are new
to the field. We first develop the mathematical tools for describing polarized
scattering of CMB photons. Then we take the reader through a detailed
derivation of the line-of-sight formalism, explaining the calculation of both
temperature and polarization power spectra due to the scalar and tensor
perturbations in a flat Universe.
