Revised with second printing, 2018.Optimization, or mathematical programming, is a fundamental subject within decision science and operations research in which mathematical decision models are constructed, analyzed, and solved.Andreasson provides a basis for the analysis of optimization models and candidate optimal solutions for continuous optimization models. Elementary but rigorous mathematics and linear algebra underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimization problems. Natural algorithms are developed from these optimality conditions, and their most important convergence characteristics are analyzed. The author answers many more "Why?" and "Why not?" than "How?" questions.The author provides lecture, exercise and reading material for a first course on continuous optimization and mathematical programming. It is geared towards third-year students, and has already been used for nearly ten years. The preface describes the main changes to the first edition.The book can be used in mathematical optimization courses at engineering, economics, and business schools. It is a perfect starting point for anyone who wishes to develop an understanding of the subject before actually applying it.