This monograph is devoted to adaptive control for nonlinear mechanical systems. The mathematical analysis of the problem of synthesizing mechanical systems is accompanied by the derivation of special control algorithms, which have many immediate, practical applications. The aim of this book is to give detailed deductions and qualitative descriptions of hindrance-resistant adaptive control algorithms for the functioning of regulated devices with tuning parameters for the realization of a given property motion. Particular emphasis is placed upon the construction of stabilized, optimal, and suboptimal adaptive controls (strategics) in the form of inverse relations, without measuring the highest derivatives. Methods are investigated to obtain an indirect adaptive control of nonlinear mechanical systems in various problems on stabilization and optimization of motion in circumstances where the exterior bounded perturbations are lacking or acting, provided that the control system parameters execute an unknown smooth drift in time.