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I will talk about the progress we have made and the challenges still facing us in the study of QCD at finite density. Due to the infamous sign problem, a direct evaluation of the partition function through lattice QCDis out of the question. Although no solution is known, a variety of partial approaches exist. I shall discuss those approaches which have been directly applied to QCD. After presenting some of the results that have been obtained, I shall also discuss what else can be done in the near future.
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