This book contains a systematic and self-contained treatment of Feynman-Kac path measures, their genealogical and interacting particle interpretations, and their applications to a variety of problems arising in statistical physics, biology, and advanced engineering sciences. With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to advanced undergraduates as well as to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research.