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This is the first of a series of papers devoted to many-body phenomena in gauge theories. We assume that weak and electromagnetic interactions are described by a spontaneously broken gauge theory and that the strong interactions are described by an asymptotically free non-Abelian gauge theory. The implications of these assumptions for the behavior of matter at finite temperature and/or chemical potential are the subject of this series of papers. Briefly, the three main areas to which our results pertain are (1) renormalization of finitetemperature field theory, (2) the equation of state of strongly interacting matter at high densities in gauge theories, and (3) elementary-particle interactions in the early universe.

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