this is a new text/reference on advanced nonlinear algorithms for mechanical systems that are based on lypaunov-type design and stability analysis. the presentation illustrates, in a unified framework, how recent lyapunov-based techniques can be used to solve a variety of nonlinear control problems for mechanical systems. starting with part one, the foundations are established in a thorough manner, including necessary math background materials. part two covers solutions to some tracking problems for rigid mechanical systems, i.e., systems modeled by ordinary differential equations. part three addresses problems of setpoint/vibration control of flexible mechanical systems, i.e., systems modeled by partial differential equations. by covering theory and applications, the book addresses both ode-based and pde-based mechanical systems and presents results for many useful real-time experiments and computer simulations.