  We develop and examine the principles governing the formation of distortions
in the cosmic microwave background. Distortions in the frequency or spectral
distribution of the background probe the thermal history of the universe
whereas those in the angular temperature distribution probe its dynamics and
geometry. Stressing model independent results, we show how the microwave
background can be used to extract information on the mass density, vacuum
density, baryon content, radiation content, expansion rate and some aspects of
structure formation in the universe. To address these issues, we systematically
develop relativistic kinetic and perturbation theory addressing issues such as
fluctuation representation, or gauge, normal mode analysis in an open geometry,
and second order effects. Through analytic and numerical results, we construct
anisotropies in a critical, open, or cosmological constant universe with
adiabatic and/or isocurvature initial conditions allowing for possible early
reionization. We find that anisotropy formation is a simple process governed by
the Compton scattering of photons and electrons and their gravitational
coupling to the other particle species in the universe.
