Set-valued analysis by covering:
This article is a presentation of an answer to the problem; deeply studied in years 1970-1980 and to a large extent unsolved then, of differential and integral calculus transfer to the framework of set-valued analysis. This transfer is achieved through the identification of the set-values maps with some families, the coverings, made up of some (class of) special functions, the representations. The process is related to the one of the atlas differential maps of the differential geometry.