In this book several concepts of synchronization are generalized and related approaches to secure communication in chaotic systems are merged. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies revealing their importance. The subsequent chapters treat recent applications. Written for audience of graduate students in applied physical sciences, systems engineers and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained textrequires only basic knowledge of integer ordinary and fractional ordinary differential equations. Design applications are illustrated with the help of several physical models of practical interest.