Spinor representation of curves on surface

This thesis consists of five chapters.In the first chapter, a short literature information about spinors and their areas of application have been given. In the second chapter some fundamental concepts and properties have been given. In the third chapter spinors have been introduced with the help of the orthonormal basis. In the fourth chapter an information about curve theory and spinor represetation of Frenet frame in three dimensional Euclidean space have been given.In the last chapter spinor represetation of curves on surface has been given with the help of the Darboux equations and spinor representations of Frenet frame and Darboux Frame have been compared.Key Words: Euclid space, curve, Frenet frame, surface, Darboux frame, spinor.