I. Fundamentals.- 1.1. Basic Concepts and Definitions.- 1.2. Sensitivity Equations and Variational Equations.- 1.3. Linear Variational Equations.- 1.4. Investigations in Phase Space.- 1.5. The Direct Method of Lyapunov.- 1.6. The Energy Method.- 1.7. Mathematical Approximation Methods.- II. Application of Stability Theory to Selected Problems of Mechanics.- 2.1. Celestial Mechanics Problems.- 2.2. Problems of the Mechanics of Rigid Bodies and of Systems.- 2.3. Problems of Elastomechanics.- Author Index.