pThis text provides a detailed and self-contained introduction to the core topics of optimal control for finite-dimensional deterministic dynamical systems. Skillfully designed to guide the student through the development of the subject, the book provides a rich collection of examples, exercises, illustrations, and applications, to support comprehension of the material. Solutions to odd-numbered exercises are included, while a complete set of solutions is available to instructors who adopt the text for their class. The book is adaptable to coursework for final year undergraduates in applied mathematics or beginning graduate students in engineering. Required mathematical background includes calculus, linear algebra, a basic knowledge of differential equations, as well as a rudimentary acquaintance with control systems. pThe book has developed out of lecture notes that were tested, adapted, and expanded over many years of teaching. Chapters 1-4 constitute the material for a basic course