Color superconductivity in quark matter

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A brief introduction into the properties of dense quark matter is given. Recently proposed gapless color superconducting phases of neutral and beta-equilibrated dense quark matter are discussed. The current status in the field is described, and the promising directions of the future research are outlined.
10 pages. Invited talk given at Workshop on Extreme QCD, Swansea, Wales, 2-5 Aug 2005. One reference added

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