The central theme of this book concerns Feynman-Kac path distributions, interacting particle systems, and genealogical tree based models. This re­ cent theory has been stimulated from different directions including biology, physics, probability, and statistics, as well as from many branches in engi­ neering science, such as signal processing, telecommunications, and network analysis. Over the last decade, this subject has matured in ways that make it more complete and beautiful to learn and to use. The objective of this book is to provide a detailed and self-contained discussion on these connec­ tions and the different aspects of this subject. Although particle methods and Feynman-Kac models owe their origins to physics and statistical me­ chanics, particularly to the kinetic theory of fluid and gases, this book can be read without any specific knowledge in these fields. I have tried to make this book accessible for senior undergraduate students having some familiarity with the theory of stochastic processes to advanced postgradu­ ate students as well as researchers and engineers in mathematics, statistics, physics, biology and engineering. I have also tried to give an "expose" of the modem mathematical theory that is useful for the analysis of the asymptotic behavior of Feynman-Kac and particle models.