  This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg
algebras and their modules. Our results may be regarded as improvements of the
attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology
theory developed here and some classical problems are pointed out, e.g.
extensions of algebras and modules, and deformation theory. The real
Koszul-Vinberg cohomology of locally flat manifolds is initiated. Thus
regarding the idea raised by M. Gerstenhaber we can state : The category of
KV-algebras has its proper cohomology theory.
