The author gives a short construction of the Steenrod operations. The method requires models for Eilenberg-MacLane spaces which have well- behaved products and actions by symmetric groups. Such models can be obtained from infinite symmetric products of spheres, or by using non- commutative differential forms. By using the latter method, the author associates complexes of differential forms with symmetric group actions to any simplicial set. These complexes are quasi-isomorphic to the non- commutative de Rham complex and they determine the Steenrod operations. The author suggests that they provide good algebraic models for homotopy types.