Reasoning under uncertainty, that is, making judgments with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. The author presents the key results on the subject, and formalizes within a unified framework the main contemporary approaches and assumptions. He concentrates on giving clear mathematical formulations, analyses, justifications, and consequences of the main theories about uncertain reasoning. Copyright (C) Muze Inc. 2005. For personal use only. All rights reserved.