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This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology and communication or laser physics. Over the last decade, a number of new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared. This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included.