L'alg`ebre de Steenrod, modules injectifs, et foncteurs polynomiaux

Lionel Schwartz

These notes come from talks made in Nantes in December 2001 at a session
" Etat de la Recherche " of the french mathematic society. They are an
introduction to the algebraic aspects of the theory of unstable modules
over the Steenrod algebra and to the relations of the related category
to functor categories. The Steenrod algebra is introduced using the
additive group scheme. Reduced injective modules are described follwing
the point of view of Campbell and Selick. Most of the material is
classical, however there are new (at least in an accessible form)
remarks concerning the odd prime case, as well as some new proofs of
classical results, in particular the structure of Miller's algebra.

The Adem relations are discussed following Bullett and MacDonald.