Probabilistic risk analysis aims to quantify the risk caused by high technology installations in situations where classical statistical analysis is difficult or impossible. This book discusses the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgment and uncertainty propagation.