The phases of QCD have presented a challenge to theoretical physics for many years. Originally it was considered folly to think about topics such as confinement, chiral-symmetry breaking, and different states of matter in relativistic field theories. Anything beyond traditional perturbation theory was met with skepticism. However, the development of semi-classical methods in field theory, the lattice-gauge formulation of the subject, and the generalizations of analytic methods of analysis from two-dimensional systems, such as duality and transitions driven by topological excitations, have changed all that.

This book is a look at the fundamentals of QCD from this perspective. After introducing lattice-gauge theory, beginning with fundamentals and reaching important recent developments, it will emphasize the application of QCD to the study of matter in extreme environments. Effective Lagrangians, which incorporate the constraints of low-energy dynamics and their symmetry realizations, will also be developed to provide a complementary, and insightful, perspective. Application of perturbative methods will also be presented in the regime of their validity.

Why extreme environments? A major theme of this book is the idea that, to understand the dynamics of QCD in ordinary circumstances, one needs to master them in extreme environments.

For example, to appreciate confinement, one can heat the system until the thermal fluctuations prevent the formation of the thin flux tubes which give rise to a linearly confining potential. In doing so, the special ingredients in the theory's dynamics which favor a vacuum pressure that squeezes flux into thin continuous tubes are emphasized.