  This paper presents a systematic treatment of the linear theory of scalar
gravitational perturbations in the synchronous gauge and the conformal
Newtonian (or longitudinal) gauge. It differs from others in the literature in
that we give, in both gauges, a complete discussion of all particle species
that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or
CDM+HDM models (including a possible cosmological constant). The particles
considered include CDM, baryons, photons, massless neutrinos, and massive
neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids
while a detailed phase-space description is given to the photons and neutrinos.
Particular care is applied to the massive neutrino component, which has been
either ignored or approximated crudely in previous works. Isentropic initial
conditions on super-horizon scales are derived. The coupled, linearized
Boltzmann, Einstein and fluid equations that govern the evolution of the metric
and density perturbations are then solved numerically in both gauges for the
standard CDM model and two CDM+HDM models with neutrino mass densities
$\onu=0.2$ and 0.3, assuming a scale-invariant, adiabatic spectrum of
primordial fluctuations. We also give the full details of the cosmic microwave
background anisotropy, and present the first accurate calculations of the
angular power spectra in the two CDM+HDM models including photon polarization,
higher neutrino multipole moments, and helium recombination. The numerical
programs for both gauges are available at http://arcturus.mit.edu/cosmics/ .
