This M. Sc . thesis is based on the following papers Surjeet. Singh , Uniform almost relative injective modules , Journal of Algebra ,4 78 , (201 7 ) 353 - 366 The concept of a module M being almost N -injective where N is a module, was introduced by Baba (1989). M is said to be almost N -injective, if for any homomorphism , A N , either f extends to a homomorphism or there exist a decomposition with and a homomorphism uch that for any , where is a projection with kernel . This concept plays a significant role is studying extending modules. A module M that is almost M -injective, is called an almost self-injective mod ule. For a given module M , the type="#_x0000_t75" , N M which cannot be extended to endomorphisms of M . In Section3 of C hapter 3 , an algebraic structure on T is given. As defined in C hapter 4 , A module M is said to be completely almost self-injective, if for any two subfactors A, B of M, A is almost B -injective. A necessary and sufficient condition for a module M to be completely almost self-injective is given. Using this, it is proved that a Von Neumann ring R is completely almost right self-injective if and only if is semi-simple and every minimal right ideal of R is injective. We have the following main result.