  We introduce a simple yet powerful {\it analytic} method which obtains the
structure of cosmic microwave background anisotropies to better than 5-10\% in
temperature fluctuations on {\it all} scales. It is applicable to {\it any}
model in which the potential fluctuations at recombination are both linear and
known. Moreover, it recovers and explains the presence of the ``Doppler peaks''
at degree scales as {\it driven} acoustic oscillations of the photon-baryon
fluid. We treat in detail such subtleties as the time dependence of the
gravitational driving force, anisotropic stress from the neutrino quadrupole,
and damping during the recombination process, again all from an analytic
standpoint. We apply this formalism to the standard cold dark matter model to
gain physical insight into the anisotropies, including the dependence of the
peak locations and heights on cosmological parameters such as $\Omega_b$ and
$h$, as well as model parameters such as the ionization history. Damping due to
the finite thickness of the last scattering surface and photon diffusion are
further more shown to be identical. In addition to being a powerful probe into
the nature of anisotropies, this treatment can be used in place of the standard
Boltzmann code where 5-10\% accuracy in temperature fluctuations is
satisfactory and/or speed is essential. Equally importantly, it can be used as
a portable standard by which numerical codes can be tested and compared.
