The q-deformation had been wide discussed in many different fields of physics and mathematics. However, all the discussions that we know of are simply based on the conformal mapping x-> qx. Throughout the thesis, we consider deformation of another kind, says q~-deformation, which is based on the mapping x-> x^q. In other words, these kinds of deformations appear in the power of variable x. We expect q~- deformation to be a new approach to the studying of Quantum Groups eventually.