Control theory for mechanical systems is a topic that has received considerable interest in the past decade, motivated by applications such as robotics and automation, autonomous vehicles in marine, aerospace and other environments, flight control, problems in nuclear magnetic resonance, micro-electro mechanical systems (MEMS), and fluid mechanics. This book presents a unified approach for studying these systems using differential geometry. The emphasis is on understanding in a geometric way all components of a mechanical control system: configuration space, the Lagrangian, external forces, and nonholonomic constraints. This book is well-suited for use as a textbook, with numerous examples and exercises included to help consolidate the theory.