: In this thesis, we establish several hereditary properties for the generalized character space of a Banach algebra . For a nonzero generalized character on , we then introduce and study vector-valued invariant -means on the space of bounded linear maps. We also establish several characterizations for existence of this means as well as several hereditary properties. In the sequel, for a nonzero character on , we study the relation between existence of topological invariant -means on duals of Banach algebras and existence of vector-valued invariant -means. Finally, for , we characterize the existence of topological invariant -mean bounded by on duals of Lipschitz algebras. Key words: Banach algebra, derivation, Lau product, locally compact groups, spectrum, topological invariant -mean, tensor product, vector-valued invariant mean.