In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring $M^*$ of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of $M^*$ can be found. In particular, two classes of ideals of $M^*$ are discussed in this paper: one is of the form $G_{M^*};(M,;N);=;{f;{in};M^*;|;f(M);{subseteq};N}$ and the other is of the form $G_{M^*};(N,;0);=;{f;{in};M^*;|;f(N);=;0}$ for a submodule N of M.