  This thesis is devoted to properties of quark matter at high density and
(comparatively) low temperature, which might exist in the interior of compact
stars. The specific heat and the quark self energy in normal quark matter are
discussed in detail. In particular higher order corrections to the known
leading order results are obtained. Also the phenomenon of color
superconductivity is discussed, with particular emphasis on the proof of gauge
independence of the fermionic quasiparticle dispersion laws. Moreover, the
expectation value of the gluon field in the 2SC and CFL phase is computed at
leading order.
