  The purpose of these notes is to provide an introduction to the Steenrod
algebra in an algebraic manner avoiding any use of cohomology operations. The
Steenrod algebra is presented as a subalgebra of the algebra of endomorphisms
of a functor. The functor in question assigns to a vector space over a Galois
field the algebra of polynomial functions on that vector space: the subalgebra
of the endomorphisms of this functor that turns out to be the Steenrod algebra
if the ground field is the prime field, is generated by the homogeneous
components of a variant of the Frobenius map.
