<P><STRONG>Part I</STRONG>: Modeling of mechanical systems; Introductory examples and problems; Linear and multilinear algebra; Differential geometry; Simple mechanical control systems; Lie groups, systems on groups, and symmetries.- <STRONG>Part II</STRONG>: Analysis of mechanical control systems; Stability; Controllability; Low-order controllability and kinematic reduction ; Perturbation analysis.- <STRONG>Part III</STRONG>: A sampling of design methodologies; Linear and nonlinear potential shaping for stabilization; Stabilization and tracking for fully actuated systems; Stabilization and tracking using oscillatory controls; Motion planning for underactuated systems; Appendices; Time-dependent vector fields; Some proofs.</P>