The main object of this dissertation is to study the endomorphism algebra of a vector space with a family of invariant subspaces. Chapter 1 contains basic definitions and results which are used in the subsequent chapters. In particular, it includes a fairly detailed account of tensor products of modules and torsion free abelian groups of rank one. Chapter 2 is devoted to the discussion of the endomorphism algebra of a finite dimensional vector space with a finite set of invariant subspaces which satisfy certain distributivity conditions. Among other results we have established original theorems (2.1) and (2.3). Chapter 3 contains· the discussion of Brenner's five-space theorem (see [4]). Finally in Chapter 4, Brenner and Butler's theorem (see [5]), which proves the existence of a certain class of torsion free abelian groups, is established.