This book is primarily aimed to be used in optimization courses at universities, engineering schools and business schools. It can be used by engineers, economists and others who work with optimization applications and optimization theory. The book describes how optimization models can be formulated and includes basic optimization theory, solution methods and practical use of the solver in Excel and the modeling language AMPL. The areas covered in the book are linear programming, network optimization, nonlinear optimization, integer programming and dynamic programming. Models and methods are illustrated with a large number of examples and figures. This is the English version of the Swedish book Optimeringslära (2008). The two versions are equivalent to each other and can easily be used in the same course for teaching in both English and Swedish. There is also a supplementary exercise book (versions in both English and Swedish) with a large number of exercises and solutions.