Appears in collection : Topos à l'IHES

The notion of sheaf over a topological space was introduced by Leray and developed by Borel, Serre and Cartan in the 1940's. A subsequent breakthrough was the appearance of the papers of Serre and Grothendieck in the 1950's. I shall describe this historical development and explain how it led Grothendieck to the introduction of toposes in his seminar SGA 4 .