This introductory textbook is primarily aimed at students of mathematics, business mathematics, and computer science, providing readers with a clear overview of the broad field of linear optimization. In addition to classical topics such as modeling, polyhedral theory, and the simplex algorithm, it also extensively covers complexity-theoretical aspects of both the simplex algorithm and polynomial methods for linear optimization. Although the latter originated in nonlinear optimization and were initially considered to have mainly theoretical value when discovered 40 years ago, today no commercial software for linear optimization can bypass these methods. The book has emerged from a study letter of the FernUniversität in Hagen and is therefore particularly suitable for self-study.