Author: Robert Hartmann, University of California Santa Cruz Title: Endo-monomial modules over $p$-groups and their classification in the abelian case (preprint) Abstract: The class of endo-monomial modules is introduced, generalizing endo-permutation modules. They can be classified by determining the monomial Dade group, and for abelian $p$-groups, this group is proven to be isomorphic to the ordinary Dade group of endo-permutation modules.