In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In this study, Quadratic Assignment Problem is handled from a polyhedral point of view. A graph theoretic formulation of the problem is presented. Later, Quadratic Assignment Polytope is defined and subsets of valid equalities and inequalities for Quadratic Assignment Polytope is given. Finally, results of the experiments with a polyhedral cutting plane algorithm using the new formulation is also presented.