The book gives a detailed and rigorous treatment of the theory ofoptimization (unconstrained optimization, nonlinear programming,semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality innonlinear programming and the theories of linear inequalities, convexpolyhedra, and linear programming are covered in detail. Over twohundred, carefully selected exercises should help the students masterthe material of the book and give further insight. Some of the mostbasic results are proved in several independent ways in order to giveflexibility to the instructor. A separate chapter gives extensivetreatments of three of the most basic optimization algorithms (thesteepest-descent method, Newton's method, the conjugate-gradientmethod). The first chapter of the book introduces the necessarydifferential calculus tools used in the book. Several chapters containmore advanced topics in optimization such as Ekeland'sepsilon-variational principle, a deep and detailed study of separationproperties of two or more convex sets in general vector spaces, Helly'stheorem and its applications to optimization, etc. The book is suitableas a textbook for a first or second course in optimization at thegraduate level. It is also suitable for self-study or as a referencebook for advanced readers. The book grew out of author's experience inteaching a graduate level one-semester course a dozen times since 1993.Osman Guler is a Professor in the Department of Mathematics andStatistics at University of Maryland, Baltimore County. His researchinterests include mathematical programming, convex analysis, complexityof optimization problems, and operations research.