This text aims to introduce set-valued and variational analysis to students in mathematics, sciences, and engineering. It illustrates the main theoretical developments with detailed case studies and examples of applications to various optimization problems, particularly optimal control problems. By including exercises and examples alongside the traditional theorem/proof format, the text emphasizes an application-driven approach to optimization and control. It is primarily written for students with a background in multivariable calculus and linear algebra, providing a brief summary of relevant concepts in functional analysis and optimization before progressing into theory, properties, and applications. The text is also suitable for practitioners in mathematics, operations research, and engineering with an interest in applying new methods to handle optimization problems with constraints. weiterlesen