Our current knowledge of the quark-gluon plasma in thermodynamical equilibrium is reviewed. The phase diagram of strongly interacting matter is discussed, with emphasis on the quark-hadron phase transition and the color-superconducting phases of quark matter. Lattice QCD results on the order of the phase transition, the thermodynamical functions, the heavy quark free energy, mesonic spectral functions, and recent results for nonzero quark chemical potential are presented. Analytic attempts to compute the thermodynamical properties of strongly interacting matter, such as perturbation theory, quasiparticle models, ``hard-thermal-loop''(HTL)-resummed perturbation theory, the Polyakov-loop model, as well as linear sigma models are discussed. Finally, color-superconducting quark matter is considered in the limit of weak coupling. The gap equation and the excitation spectrum are derived. The solution of the gap equation, gap parameters in various color-superconducting phases, and critical temperatures for the transition to normal-conducting quark matter are presented. A summary of gluon and photon properties in color superconductors is given.

89 pages, 26 figures, review for Prog. Part. Nucl. Phys, minor revisions to text, correction of typos, refs. added