Connections on noncommutative graded spaces

In this thesis some common concepts of classical algebra and differantial geometry are analyzed within the context of the noncommutative graded spaces. This study consists of six parts. In the first part, the literature and the aim of thesis are given. In the second part, algebraic basic definitions are mentioned. In the third part, graded algebraic structures are given. In the fourth part, the definition and the properts of Lie super algebra are discussed. In the fifth part, comutation factor, Schur multiplier and the relationship between them is discussed.Moreover, the definitions about graded algebraic structures are given and some theorems, lemmas have been proved. In addition, the diferantial calculus based on derivations and connections have been studied. Finally, conclusions and recommendations are discussed.