Two methods of generalizing the classical Noetherian theory to modules over arbitrary rings are described in detail. The first is by extending the primary ideals and isolated components of Murdoch to modules. The second is by using the tertiary sub-modules of Lesieur and Croisot. The development is self-contained except for elementary notions of ring and module theory. The definition of primal submodules with some results is included for completeness. Some concrete examples are given as illustrations. / Science, Faculty of / Mathematics, Department of / Graduate