This self-contained book provides a systematic account of the main algorithms derived from the simplex method and the means by which they may be organized into effective procedures for solving practical linear programming problems on a computer. The book begins by characterizing the problemand the method used to solve it, going on to deal with the practicalities of the subject, emphasizing concerns of implementation. The final section of the book discusses the basic principles of optimization: duality, decomposition, and homotopy. In conjunction with the simplex method, they eachlead to other key algorithms of linear programming. The author's approach is distinguished by his detailed exploration of ideas and issues that center on the need to structure data suitably, and to organize calculations in an efficient and numerically stable manner. Unlike many liner programmingtexts, the author's overall perspective is grounded in nonlinear programming rather than combinatorics.