This chapter includes the main components necessary to formulate the dynamics of planar multibody systems. In this process, the fundamental issues associated with embryogenesis of multibody systems are presented. The main types of coordinates utilized in the formulations of general planar multibody systems are described. In addition, the fundamental characteristics of some relevant constraint equations are also presented in this chapter. Then, the key aspects related to the dynamic analysis of planar multibody mechanical systems are discussed. The formulation of multibody system dynamics adopted here uses the generalized absolute coordinates to derive the multibody system equations of motion. This formulation results in the establishment of a mixed set of ordinary differential and algebraic equations, which are numerically solved in order to predict the dynamic behavior of multibody systems.