This first lecture will be devoted to review the main properties, results and methods concerning Linear Programming, one fundamental topic of Optimization. After having gone over the definition and the fundamental geometric properties of linear programming, we are going to overview the simplex method, which is the most well known procedure for solving it. Then the concept of dual problem will be introduced together with the main duality results valid for linear programming. Finally we are going to look at how, in particular cases, even linear programming problems with a huge number of variables can be solved with the simplex method through the so called column generation approach.