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Optimization is an important tool in decision science and in the analysis of physical systems. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This book covers numerical methods for finite-dimensional optimization problems involving fairly smooth functions. It concentrates on methods for unconstrained optimization, with attention given at the end to problems with constraints. The approach taken is natural and reasonable, beginning with very simple ideas and progressing through more complicated concepts. Both authors are well known and highly regard in the numerical optimization community. The book will be useful as a text for a graduate course, or as a reference for practioners' use. It should be accessible to students at the master's degree level in engineering, mathematics, and other related areas.