Abstract
In this paper, some of the main problems of harmonic analysis on perfect hypergroups are completely solved. Many ways to preserve the perfectness of hypergroups under different kinds of transformations are given. Some properties of the set of Radon measures on perfect hypergroups are shown. Moreover, exact conditions on translation operators to translate perfect hypergroups to another perfect hypergroups are explained. Rigorous computations with implemented formal examples are explicitly introduced. (C) 2016 Physics Essays Publication.