First part (Linear Programming): Linear programming problem and its standard form. The fundamental theorem of linear programming. The simplex method (non-degenerate and degenerate cases). Two-phase method. Duality. Second Part (Non Linear Programming): Convex sets. Separation and Alternative Theorems. Convex functions. Convex Programming. Saddle-Point Characterization. The F.John and the Kuhn-Tucker Optimality conditions. The Zoutendijk and the Topkis-Veinott algorithms.