This monograph is an introduction to the theory of the dynamics metastable and unstable states. This is an active branch of research which many fundamental questions remain unanswered. Therefore our discussion of the theory is by necessity incomplete. We do attempt, however, to discuss the basic ideas so far formulated in order that the reader can have an overall view of the current state of the theory. We do not give an exhaustive list of references to the theoretical and experimental work in this field, since recent reviews on this subject (which are mentioned in the text) are reasonably comprehensive. We do, however, provide a list of selected references for further study at the end of each chapter.