Dr. Alan J Hoffman is a pioneer in linear programming, combinatorial optimization, and the study of graph spectra. In his principal research interests, which include the fields of linear inequalities, combinatorics, and matrix theory, he and his collaboratorics, and matrix theory, he and his collaborators have contributed fundamental concepts and theorems, amany of which bear their names. This volume of Dr. Hoffman's selected papers is divided into seven sections: geometry; combinatorics; matrix inequalities and eigenvalues; linear inequalities and linear programming; combinatorial optimization; greedy algorithms; graph spectra. Dr. Hoffman has supplied background commentary and anecdotal remarks for each of the selected papers. He has also provided autobiogrphical notes showing how he chose mathematics as his profession, and the influences and motivations which shaped his career. Contents: The Variation of the Spectrum of a Normal Matrix (with H W Wielandt); Integral Boundary Points of ConvexPolyhedra (with J Kruskal); On Moore Graphs with Diameters 2 and 3 (with R Singleton); Cycling in the Simplex Algorithm; On Approximate Solutions of Systems of Linear Inequalities; On the Polynomial of a Graph; Some Recent Applications of the Theory of Linear Inequalities of Extrenal Combinatorial Analysis; and 37 other papers. Readership: Researchers in linear programming and inequalities, combinatorics, combinatorial optimization, graph theory, matrix theory and operations research.