A system of rigid bodies in the sense of this book may be any finite number of rigid bodies interconnected in some arbitrary fashion by joints with ideal holonomic, nonholonomic, scleronomic and/or rheonomic constraints. Typical examples are the solar system, mechanisms in machines and living mechanisms such as the human body provided its individual members can be considered as rigid. Investigations into the dynamics of any such system require the formulation of nonlinear equations of motion, of energy expressions, kinematic relationships and other quantities. It is common practice to develop these for each system separately and to consider the labor necessary for deriving, for example, equations of motion from Lagrange's equation, as inevitable. It is the main purpose of this book to describe in detail a formalism which substantially simplifies these tasks. The formalism is general in that it provides mathematical expressions and equations which are valid for any system of rigid bodies. It is flexible in that it leaves the choice of generalized coordinates to the user. At the same time it is so explicit that its application to any particular system requires only little more than a specification of the system geometry. The book is addressed to advanced graduate students and to research workers. It tries to attract the interest of the theoretician as well as of the practitioner.