This book gives a comprehensive up-to-date presentation of some of the classical areas of reliability. It is based on a more advanced probabilistic framework using the modern theory of stochastic processes. This framework allows the analyst to formulate general failure models, establish formulas for computing various performance measures, and determine how to identify optimal replacement policies in complex situations. A number of special cases analyzed previously can be included in this framework. This book presents a unifying approach to some of the key areas of reliability theory, summarizing and extending results obtained in recent years. Although conceived mainly as a research monograph, this book can also be used for graduate courses and seminars. It primarily addresses probabilists and statisticians with research interests in reliability.