This book discusses the physical phases of Quantum Chromodynamics (QCD) in ordinary environments, as well as in extreme environments with high temperatures and high baryon numbers. Under such extreme conditions, new phases are thought to exist: the quark-gluon plasma and color superconductivity. After introducing lattice gauge theory, John Kogut and Mikhail Stephanov emphasize the application of QCD to the study of matter in extreme environments through a host of methods. These include lattice gauge theory, lower dimensional model field theories and effective Lagrangians.