Color Superconductivity in High Density Quark Matter

We review recent progress on the phenomena of color superconductivity in high density quark matter. We begin with a brief overview of the unique aspects of physics near a Fermi surface and the implications for renormalization group (RG) techniques. We next discuss the qualitative differences between asymptotic densities, where the effective coupling constant can be made arbitrarily small, and intermediate densities where quark matter is still strongly coupled. It is in the latter regime where RG techniques are particularly useful, in that they yield a generic description of possible behaviors without relying on an expansion in the strong coupling constant. Finally, we discuss aspects of the QCD groundstate at asymptotic densities, which can be determined in a systematic weak coupling expansion.