Phases of QCD at High Baryon Density

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We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.
15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 2000

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