  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.
