This book is a comprehensive introduction to the techniques needed to produce realistic simulations and animations of particle and rigid body systems. It focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic simulation engines that can be used to generate convincing animations of physical events involving particles and rigid bodies, such as a jet flow of water pushing dry flowers away on a patio. It can also be used to produce accurate simulations of mechanical systems, such as a robotic parts feeder where parts are dropped on a conveyer belt and are positioned and aligned as they hit fences strategically placed on the conveyer and used to align the parts to a specific orientation. The book was written for computer graphics, computer animation, computer-aided mechanical design, and modeling software developers who want to learn and incorporate physically based dynamic simulation features in their own systems. All mathematical algorithms and implementations are described in detail in the appendices.