The objective of the book is to make optimal control theory accessible to a large class of engineers and scientists who are not mathematicians, although they have a basic mathematical background, but who need to understand and want to appreciate the sophisticated material associated with optimal control theory. Therefore, the material is presented using elementary mathematics, which is sufficient to treat and understand in a rigorous way the issues underlying the limited class of control problems in this text. Furthermore, although many topics that build on this foundation are covered briefly, such as inequality constraints, the singular control problem, and advanced numerical methods, the foundation laid here should be adequate for reading the rich literature on these subjects.