The dual linear programming problem is constructed from the cost and constraints of the original linear programming problem or their primal linear programming problem. Linear programming problem is solved by the simplex method. Therefore, a dual linear programming problem can also be solved using the simplex method because every dual linear programming problem is a linear programming problem. Duality is used to improve the performance of the simplex algorithm. It helped to develop non-simplex algorithms such as Karmarkar's algorithm and Khachiyan's algorithm. Lemke and Beale in 1954 designed a dual version of the simplex method. This chapter discusses some basic properties of dual problems. It begins with the weak duality theorem. The dual simplex method is used when there is no obvious basic feasible solution to the linear programming problem. The chapter presents the step by step algorithm for dual simplex method.