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The book offers a comprehensive overview of controllability problems and minimum energy control for broad classes of dynamical systems, including linear, semilinear and nonlinear systems, which are important for modeling systems in automatic control, electrical engineering, mechanics and informatics. It develops the theory of controllability for both finite and infinite dimensional dynamical systems described by differential state equation, and studies in detail functional analysis and matrix algebra, which provide essential and effective tools for the new solutions of a number of important controllability problems. The theoretical results are illustrated by examples throughout the book. Primarily intended for academic researchers working in mathematical control theory, the self-contained text is easily accessible and particularly interesting for control engineering and applied mathematics graduates.