Suppose that R is a finite dimensional algebra and T is a right R-modu
le. Let A=End(R)(T) be the endomorphism algebra of T. This paper prese
nts a systematic study of the relationships between the representation
theories of R and A, especially those involving actual or potential q
uasi-hereditary structures on the tatter algebra. Our original motivat
ion comes from the theory of Schur algebras, work of Soergel on the Be
rnstein-Gelfand-Gelfand category Omicron, and recent results of Dlab-H
eath-Marko realizing certain endomorphism algebras as quasi-hereditary
algebras. Besides synthesizing common features of all these examples,
we go beyond them in a number of new directions. Some examples involv
e new results in the theory of tilting modules, an abstract ''Specht/W
eyl module'' correspondence, a new theory of stratified algebras, and
a deformation theory based on the study of orders in semisimple algebr
as. Our approach reconceptualizes most of the modular representation t
heory of symmetric groups involving Specht modules and places that the
ory in a broader context. Finally, we formulate some conjectures invol
ving the theory of stratified algebras and finite Coxeter groups.