This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abstract theory to its use in concrete problems. It offers a working knowledge of relevant techniques, plus an impetus for further study. Starting with an overview of fundamental problems and theories, the text advances to illustrative examples and examinations of variable end-points and the fundamental sufficiency theorem. Subsequent chapters explore the isoperimetrical problem, curves in space, the problem of Lagrange, and the parametric problem. The final chapter is devoted to multiple integrals, with a particular focus on Dirichlet's principle. Suitable for advanced undergraduate and graduate students, this text requires a background in mathematical analysis.