In this paper we construct universal infinite dimensional formal group laws and formal A-modules, This requires the consideration of formal group laws and formal A-modules over topological rings because universal infinite dimensional formal group laws and formal A-modules over discrete rings obviously cannot exist. The main motivation for these constructions is the classification theory for formal A-modules. Two of the main operators in this theory "q-typification" and fff, a Frobenius type operator, are defined via the universal example making it desirable to have also infinite dimensional universal objects. This is all the more desirable because the proofs for the classification theory, even for finite dimensional formal A-modules only, unavoidably involve infinite dimensional formal A-modules.