This book presents a fairly complete account of the theory of optimization when both maximands and constraints are smooth functions of a finite number of variables. The theories of mathematical programming with scalar and with vector criteria are discussed. The book also provides a rigorous introduction to variational problems and clarifies many of the issues that have been clouded by the hasty application of mathematical results to economics. The theory of infinite-dimensional optimization is also surveyed. In addition, a lot of attention is paid to the history of optimization theory. Many examples are drawn from microeconomic theory and from the author's work on the applications of optimal control theory to dynamic and static economic theory. Numerous numerical and graphical illustrations are included.