Abstarct: Topological indices are real numbers‎, ‎which are identical in isomorph graphs.The Wiener index‎, ‎which is shown by $ W $ is the first topological index that has been used to determine some of physical and chemical properties of the materials.In this thesis‎, ‎Wiener index is studied on trees and unicyclic graphs.In this regard‎, ‎the minimum value of the Wiener index is investigated on the both trees and unicyclic graphs with fixed diameter‎.