Reference for graduate students, covering the physical phases of quantum chromodynamics (QCD).This book discusses the physical phases of Quantum Chromodynamics (QCD) in ordinary environments, as well as in extreme environments of high temperatures and high baryon number. Under such extreme conditions, new phases are thought to exist: the quark-gluon plasma and colour superconductivity. After introducing lattice gauge theory, beginning with fundamentals and reaching important recent developments, this book emphasizes the application of QCD to the study of matter in extreme environments through a host of methods, including lattice gauge theory, lower dimensional model field theories and effective Lagrangians.This book discusses the physical phases of Quantum Chromodynamics (QCD) in ordinary environments, as well as in extreme environments of high temperatures and high baryon number. Under such extreme conditions, new phases are thought to exist: the quark-gluon plasma and colour superconductivity. After introducing lattice gauge theory, beginning with fundamentals and reaching important recent developments, this book emphasizes the application of QCD to the study of matter in extreme environments through a host of methods, including lattice gauge theory, lower dimensional model field theories and effective Lagrangians.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.1. Introduction; 2. Background to spin systems and critical phenomena; 3. Gauge fielƒ=