This course provides an introduction to linear programming a tool widely used in operations research. A linear program is the problem dealing with the optimization of a linear function subject to a number of constrains. The first objective of the course is to learn what a linear program is and learn to recognize it in "real world problems". We will learn how to solve it using the simplex method. The study of the simplex method will involve duality theory, implementation issues, mesuring the efficiency of the algorithms, and other related topics. We conclude the course with applications of linear programming to game theory and network flows. If time permits we will also address integer programming and interior point methods.