The problems of quark confinement, chiral-symmetry breaking, and strongly interacting matter in extreme environments are converging and much is being learned, both experimentally and theoretically. We hope that this book helps researchers find common ground in this developing field.

The breadth of the field is quite remarkable. Concepts from critical behavior, effective-field theory and random-matrix models, lattice-gauge theory and numerical methods, spin models and duality, equilibrium and nonequilibrium thermodynamics, and even string theory play important roles here. It is impossible to tell which approach will lead to the next major advance in the field.

The field depends on a “new culture” in theoretical physics, one in which theorists use lattice-gauge theory as a realistic laboratory to test new ideas through numerical methods and computer simulations.The theorist is no longer limited, in many but, alas, not all cases, to unrealistic models for concrete inspiration. Lattice-gauge simulations have led to the sharpening of several approaches to QCD that have influenced the field very productively. We can look forward to the development of new algorithms that can address SU(3) QCD at nonzero baryon chemical potential and find new states of matter at high densities.