1. Introduction -- 2. The Simplex Algorithm -- 3. Geometry -- 4. The duality theorem -- 5. Matrix environment -- 6. General form -- 7. Unsolvable systems -- 8. Geometry revisited -- 9. Game theory -- Network environment -- 11. Combinatorics -- 12. Economics -- 13. Integer optimization -- A. Linear algebra review -- B. Equivalence of auxiliary and shortcut methods -- C. Complexity -- D. Software.