This book presents a general methodology for dynamic analysis of planar rigid multibody systems. After a brief characterization of the embryogenesis of multibody systems, the concept of multibody system is presented and accompanied with some examples of application. The main types of coordinates used to model multibody systems are also presented and discussed. A description of global and local coordinates is also offered. Then, a complete formulation of the elementary kinematic constraints is presented, as well as the main issues related to the kinematic analysis of multibody systems. Then, the basic external forces that can be present in multibody systems are briefly described. The formulation of the general equations of motion for constrained multibody is also included. In the sequel of this process, the main numerical methods used in both kinematics and dynamics of multibody systems are reviewed. Subsequently, a complete formulation of the Baumgarte stabilization method is offered, in which some techniques used in the selection of the Baumgarte parameters are analyzed. Finally, this book includes a full list of references.