Multibody systems investigated in the book are composed of rigid bodies. The bodies are interconnected in an arbitrary configuration by joints and force elements of arbitrary nature. Typical examples of multibody systems are linkages in machines, vehicles and industrial robots. A characteristic feature of the formalism presented is the application of graph-theoretical concepts. The interconnection structure of a multibody system is mapped onto a graph whose vertices and arcs represent bodies and interconnections of bodies, respectively. Codes based on the formalism have found important applications in the automotive industry and in other branches of engineering. Special systems investigated in the book are systems with tree-structure, systems with revolute joints only, systems with spherical joints only, systems with nonholonomic constraints and systems in planar motion. By applying the said concepts of graph theory to linear oscillators new formulations are found for mass-, damping and stiffness matrices. A separate chapter is devoted to the problem of collision of a multibody system either with another multibody system or with itself. Introductory chapters deal with basic elements of rigid body kinematics and dynamics. A short chapter is devoted to classical, analytically soluable problems of rigid body dynamics. This book is addressed to graduate students and to R & D engineers.