This book, "Theory of Linear and Integer Programming" by Alexander Schrijver, is a comprehensive resource on linear and integer programming. It is published by John Wiley & Sons and is available in multiple international locations. The book is structured into several parts, covering linear algebra, lattices and linear Diophantine equations, polyhedra, linear inequalities, and linear programming, followed by integer linear programming. The first part introduces linear algebra and complexity, discussing Gaussian elimination and iterative methods. The second part explores lattices and linear Diophantine equations, including the Hermite normal form and basis reduction. The third part delves into polyhedra, linear inequalities, and linear programming, covering fundamental concepts, the structure of polyhedra, polarity, and the theoretical complexity of linear programming. The fourth part focuses on integer linear programming, discussing integral polyhedra, totally unimodular matrices, cutting planes, and various solution methods such as branch-and-bound and Lagrangean relaxation. The book also includes historical notes, further notes, and references, along with indexes for notation, authors, and subjects. The content is detailed and technical, providing a thorough understanding of linear and integer programming, including algorithms, complexity, and applications. It is suitable for advanced students and researchers in mathematics, computer science, and operations research.This book, "Theory of Linear and Integer Programming" by Alexander Schrijver, is a comprehensive resource on linear and integer programming. It is published by John Wiley & Sons and is available in multiple international locations. The book is structured into several parts, covering linear algebra, lattices and linear Diophantine equations, polyhedra, linear inequalities, and linear programming, followed by integer linear programming. The first part introduces linear algebra and complexity, discussing Gaussian elimination and iterative methods. The second part explores lattices and linear Diophantine equations, including the Hermite normal form and basis reduction. The third part delves into polyhedra, linear inequalities, and linear programming, covering fundamental concepts, the structure of polyhedra, polarity, and the theoretical complexity of linear programming. The fourth part focuses on integer linear programming, discussing integral polyhedra, totally unimodular matrices, cutting planes, and various solution methods such as branch-and-bound and Lagrangean relaxation. The book also includes historical notes, further notes, and references, along with indexes for notation, authors, and subjects. The content is detailed and technical, providing a thorough understanding of linear and integer programming, including algorithms, complexity, and applications. It is suitable for advanced students and researchers in mathematics, computer science, and operations research.