In this thesis, we study ?-injective modules. The purpose of this thesis is to provide the new characterization for an injective module to be ?-injective. All rings have identity elements and all modules are unitary right R-modules. At first, it is introduced the concept of ?-injective. A module M is said to be ?-injective provided that is injective for any cardinal where it is denoted by the direct sum of copies of M. For an injective module M, the following are equivalent: (1) M is ?-injective. (2) M is countable ?-injective. (3) R satisfies ascending chain condition on the set of right ideals I of R that are annihilators of subsets of M. (4) M is a direct sum of indecomposable ?-injective. It is shown that an injective module M is ?-injective if and only if there exists an infinite cardinal uch that every essential extension of is a direct sum of injective modules. The important purpose of this thesis is to extend the above theorem and to provide the new characterization for an injective module to be ?-injective in terms of the direct sums of injective modules and projective modules. As a consequence, it is obtain that an injective module M is ?-injective if and only if each essential extension of is a direct sum of modules that are either injective or projective. It also follows that an arbitrary module M is ?-injective if and only if each essential extension of is a direct sum of injective modules. It is well known that a ring R is right noetherian if and only if every direct sum of injective right R-modules is injective. From this it follows that a ring R is right noetherian if and only if each injective right R-module is ?-injective. In addition, it is shown that if R is an integral domain then the injective hull E(R R ) of R is ?-injective if and only if R is a right Ore domain. Also if R is a nonsingular ring, then E(R R ) is ?-injective if and only if R satisfies the ascending chain condition on complement right ideals.