The book provides an introduction to central concepts and methods of nonlinear optimization. It is based on lectures by the authors at the Technical University of Munich, the Technical University of Darmstadt, and the University of Hamburg. The content of the book is specifically tailored to mathematical bachelor's programs and has proven to be a solid foundation for corresponding lectures as well as for subsequent in-depth study in the field of optimization. The scope corresponds to two two-hour lectures or one four-hour lecture, covering both unconstrained optimization problems and optimization problems with constraints in roughly equal measure. In the section on unconstrained optimization, both trust-region and line search methods for globalization are discussed. For the latter, a concept of feasible search directions and step sizes that is both powerful and intuitive is developed.