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This is a short introductory course on geometric control theory with emphasis on controllability and optimal control problems. This direction of mathematical control theory originated in the 1970s; it actively employs methods of differential geometry, Lie groups and Lie algebras, and symplectic geometry for the study of control systems. The main literature on this subject are the books by V. Jurdjevic [26], A. Agrachev and the author [3], H. Schättler and U. Ledzewicz [34], and a very recent book by A. Agrachev, D. Barilari, and U. Boscain [2] (in chronological order). The course aims to give a very concise first impression on the circle of problems, methods, and results of geometric control theory, and to advance problem solving skills employing these methods and results. The book is intended for a wide readership, starting from undergraduate students in mathematics and applied mathematics to experts in “classic” control theory, for whom geometric methods might be new. The book may serve as a textbook for a semester or half-semester special course for students starting from the undergraduate level, as was done by the author in universities of Pereslavl-Zalessky, Moscow, Novosibirsk, Sochi, Trieste, Rouen, Brno, Bra¸sov, Jyväskylä, Changchun, and Shanghai. We aim to achieve the following goals in this book: • Low initial prerequisites for readers • Problem-oriented exposition • Theoretical minimalism: only the theory absolutely necessary to start geometric control is included • Active use of illustrations • Relatively concise volume • Inclusion of some advanced, recently published material