This monograph, "Foundations of Bilevel Programming," by Stephan Dempe, focuses on the theoretical foundations of bilevel programming problems. Bilevel programming is a hierarchical optimization problem where the constraints include a second, parametric optimization problem. The book covers various aspects of bilevel programming, including its applications in economic game theory, chemical equilibria, environmental economics, and more. It delves into linear bilevel problems, parametric optimization, optimality conditions, solution algorithms, and discrete bilevel problems. The author emphasizes the complexity of bilevel programming, highlighting its NP-hard nature and the challenges in formulating and solving such problems. The book aims to provide a comprehensive overview of the field, suitable for applied mathematicians, operations researchers, and advanced undergraduate students. It includes detailed proofs and a thorough overview of results in parametric nonlinear optimization, along with numerous applications to illustrate the wide range of potential uses.This monograph, "Foundations of Bilevel Programming," by Stephan Dempe, focuses on the theoretical foundations of bilevel programming problems. Bilevel programming is a hierarchical optimization problem where the constraints include a second, parametric optimization problem. The book covers various aspects of bilevel programming, including its applications in economic game theory, chemical equilibria, environmental economics, and more. It delves into linear bilevel problems, parametric optimization, optimality conditions, solution algorithms, and discrete bilevel problems. The author emphasizes the complexity of bilevel programming, highlighting its NP-hard nature and the challenges in formulating and solving such problems. The book aims to provide a comprehensive overview of the field, suitable for applied mathematicians, operations researchers, and advanced undergraduate students. It includes detailed proofs and a thorough overview of results in parametric nonlinear optimization, along with numerous applications to illustrate the wide range of potential uses.