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.