Abstract: Let A be an artin algebra. The lecture will report on the work of M. Auslander in his seminal Philadelphia Notes (published already in 1978), where he exhibited his theory of morphisms determined by modules. This theory has to be considered as an exciting frame for describing the poset structure of the category of A-modules. The main idea is to identify any right C-factorization lattice with the submodule lattice of a finite length B-module, where B is again an artin algebra. As a consequence, we can use the Jordan-Hoelder theorem for finite length modules in order to deal with factorizations of morphisms. In case we deal with k-algebras, were k is an algebraically closed field, any right C-factorization lattice is the disjoint union of finitely many projective varieties and these varieties are isomorphic to quiver Grassmannians.