Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin"s minimum principle, and numerical techniques for trajectory optimization. Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin"s minimum principle are the subjects of chapters 4 and 5, and chapter 6 examines iterative numerical techniques for finding optimal controls and trajectories. Numerous problems, intended to introduce additional topics as well as to illustrate basic concepts, appear throughout the text.