This text was developed from course notes written by Michael Patriksson and used over several years at Chalmers University of Technology. The book's main focus is on providing a basis for the analysis of optimization models and of candidate optimal solutions, especially for continuous (even differentiable) optimization models. The main part of the mathematical material therefore concerns the analysis and algebra that underlie the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. Starting with a brief Introduction, the text covers fundamentals, optimality conditions, linear programming, and algorithms. The final chapter consists of exercises, for which solutions are provided. Suitable for advanced undergraduates and graduate students of mathematics/operations research, the treatment requires some background in linear algebra, real analysis, and logic. This new third edition features subsequent revisions and represents a further expansion of the original text.