Intended as an introduction to the many topics covered by the term optimization, this text places special emphasis on applications in industry. The first part of the book covers unconstrained optimization, describing the main techniques for solving problems both for functions of only one variable, and for multi-variable functions, with emphasis placed on the practical problems of why and how methods succeed or fail, rather than on rigorous proofs. The second part describes the methods used to solve linear programming problems, giving applications in industry and outlining the simplex and dual simplex methods. The third part covers nonlinear programming, integer programming and dynamic programming, showing how the techniques of linear programming can be extended to deal with nonlinearity and discrete entities. Intended for senior undergraduate and graduate students studying optimization, it assumes no detailed mathematical knowledge.