I Introduction to Linear Programming -- II Dual Linear Programs -- III Elements of the Theory of Linear Systems -- IV Bases and Basic Solutions of Linear Programs -- V The Simplex Algorithm -- VI The Two Phases of the Simplex Method: Theoretical Results Proved by Application of The Simplex Method -- VII Computational Aspects of the Simplex Method: Revised Simplex Algorithm; Bounded Variables -- VIII Geometric Interpretation of the Simplex Method -- IX Complements on Duality: Economic Interpretation of Dual Variables -- X The Dual Simplex Algorithm: Parametric Linear Programming -- XI The Transportation Problem -- References -- Aide Memoire and Index of Algorithms.