This introductory text offers a far-reaching, rigorous, application-oriented approach to variational theory that will increase students' understanding of more specialized books and research papers in the field. The treatment acquaints readers with basic methodology, selecting a path through classical conditions for an extremum, modern existence theory, and problems of recent origin and with novel features. Numerous examples from engineering, physics, and other diverse areas receive full treatment. The first six chapters require no special preparation beyond a familiarity with advanced calculus. Chapter 1 features a survey of the prerequisite concepts and results, which may be consulted as needed. Subsequent chapters demand greater mathematical maturity, drawing from the fields of modern real analysis, theory of differential equations, functional analysis, and topology. However, the book is sufficiently self-contained that those without such a background can still master much of the second half. Ideal as a primary or supplementary text, this volume imparts fundamental knowledge of a field with widespread, profound implications while challenging readers to develop greater insights.