In this chapter, we introduce the simplex algorithm for solving linear programming problems. We confine the chapter to Phase II pivoting, which is valid for any standard form maximization problem. We handle standard form minimization problems by using duality, since the dual problem of a standard form minimization problem is a standard form maximization problem. Since all linear programming problems that arise in game theory are standard form, the material of this chapter is sufficent to study game theory. Phase I pivoting, which is used for problems with mixed constraints, and integer programming are deferred until a later chapter, after we explore game theory. We end the chapter with a section on using software packages such as Microsoft Excel and Wolfram Mathematica to solve linear programming problems.