Basic properties of rings. Ideals and quotient rings. Ring Homeomorphisms. Polynomial rings. Left and right modules. Free modules. Direct sums of modules. Finitely generated modules over a p.i.d. Artinian and Noetherian modules. Completely reducible modules. Tensor product of modules. Bimodules. Algebras and coalgebras. Projective and injective modules. Primitive and semi-primitive rings. The radical of a ring. Prerequisite: MAT 621.