Intense external fields destabilize vacuum by introducing the creation of particle pairs. In this book the formalism of quantum electrodynamics (QED), using a special perturbation theory with matrix propagators, is systematically analyzed for such systems. The developed approach is, however, general for any quantum field with unstable vacuum. In addition to a description of the theory, the authors propose solutions for real pair-creating fields. They discuss the general form for the causal function and many other Green functions, as well as methods for finding them. Analogies for the optical theorem and rules for computing total probabilities are given, as are solutions for non-Abelian theories.