We have started our study of the cohomology of categories [1] in particularizing a note of C. Ehresmann [2]. Then, our wislı was to put together, in a same work, our original study and the theory of M. Andre [3 ]. The result is the text herewith presen- ted. In the first chapter, we construct a homology and a coho- mology of categories. The cohomology is a generalization (dif- ferent of the one defined in [2]) of the cohomology considered in [1]. The homology is the very same as the one defined in [3]. In the second chapter, we particularize the previous theory in order to obtain a cohomology of the smaU categories which generalizes the classical cohomology of the groups, a group heing a particular category. These two chapters are written in a different mind; conse- quently, we have judged useful to differentiate their notations. We could use also the tools herewith introduced, for example, in a generalization of the study of the groups operating on topo- logical spaces; this wiU be the subject of an other publication.