  The purpose of this article is to introduce projective geometry over
composition algebras : the equivalent of projective spaces and Grassmannians
over them are defined. It will follow from this definition that the projective
spaces are in correspondance with Jordan algebras and that the points of a
projective space correspond to rank one matrices in the Jordan algebra. A
second part thus studies properties of rank one matrices. Finally, subvarieties
of projective spaces are discussed.
