  This paper introduces a systematic treatment of the linear theory of scalar
gravitational perturbations in the presence of a fully inhomogeneous magnetic
field. The analysis is conducted both in the synchronous and in the conformally
Newtonian gauges. The cosmological plasma is assumed to be composed of cold
dark mattter, baryons, photons, neutrinos. The problem of super-horizon initial
conditions for the fluid variables of the various species and for the coupled
system of Boltzmann-Einstein equations is discussed in the presence of an
inhomogeneous magnetic field. The tight coupling approximation for the
Boltzmann hierarchy is extended to the case where gravitating magnetic fields
are included.
