This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "e;the calculus of variations"e;) and more modern topics (under the heading of "e;optimal control"e;). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.