These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.

Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel Dubois-Violette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of N-differential modules and N-complexes. Several applications and examples coming from physics are discussed. The commun feature of these physical applications is that they deal with the theory of constrained or gauge systems. In particular different aspects of the BRS methods are explained and a detailed account of the N-complexes arising in the theory of higher spin gauge fields is given. 1.

Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel Dubois-Violette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of N-differential modules and N-complexes. Several applications and examples coming from physics are discussed. The commun feature of these physical applications is that they deal with the theory of constrained or gauge systems. In particular different aspects of the BRS methods are explained and a detailed account of the N-complexes arising in the theory of higher spin gauge fields is given. 1.