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Optimal control theory is a mathematical optimization method with important applications in the aerospace industry. This graduate-level textbook is based on the author’s two decades of teaching at Tel-Aviv University and the Technion Israel Institute of Technology, and builds upon the pioneering methodologies developed by H. J. Kelley. Unlike other books on the subject, the text places optimal control theory within a historical perspective. Following the historical introduction are five chapters dealing with theory and five dealing with primarily aerospace applications.