1. Introduciton 1. Variants of the linear programming problem 2. Examples of linear programming problems 3. Piecewise linear convex objective functions 4. Graphical representation and solution 5. Linear algebra background and notation 6. Algorithms and operation counts 7. Excercises 8. History, notes, and sources 2. The geometry linear programming 1. Polyhedra and convex sets 2. Extreme points, vertices, and basic feasible solutions 3. Polyhedra in standard form 4. Degeneracy 5. Existence of extreme points 6. Optimality of extreme points 7. Representation of polyhedra: Fourier-Motzkin elimination 8. Summary 9. Excercise 10. Notes and sources 3. The simplex method 1. Optimality conditions 2. Development of the simplex method 3. Implementations of the simplex method 4. Anticycling: lexicography and Bland's rule 5. Finding an initial basic feasible solution 6. Column geometry and the simplex method 7. Computational efficiency of the simplex method 8. Summary 9. Exercises 10. Notes and sources 4. Duality theory 1. Motivation 2. The dual 5. Sensitivity analysis 6. Large scale optimization 7. Network flow problems 8. Complexity of linear programming and the ellipsoid method 9. Interior point methods 10. Integer programming formulations 11. Integer progamming methods 12. The art in linear optimization