This work provides the essential foundations for modular construction of (typed) unification grammars for natural languages. Much of the information in such grammars is encoded in the signature, and hence the key is facilitating a modularized development of type signatures. We introduce a definition of signature modules and show how two modules combine. Our definitions are motivated by the actual needs of grammar developers obtained through a careful examination of large scale grammars. We show that our definitions meet these needs by conforming to a detailed set of desiderata.