Curves and surfaces in inversive geometry

This thesis consist of four chapters.In the first chapter; some fundamental definitions and theorems are given.In the second chapter; some relationships and characterizations are examined between the inversive surfaces by giving the concept of inversion, inversive curve, inversive surface definitons.In the third chapter; original works have been done, the relationships have been calculated the bases of the tangent spaces, the shape operators and Christoffel symbols of the between inversive surfaces. Also, some properties which are invariant of inversive surfaces under inversion mapping are obtained.In the fourth chapter; some applications were done about the subject