This M.Sc. thesis is based on the following papers: • ALAHMAD, A. AND JAIN, S.K., A note on almost injective modules, Math. J. Okayama Univ, 51, (2009), 101–109. •SINGH, S., Almost relative injective modules, Osaka J. Math, 53(2016) 423–438. The work in this thesis is prompted by the idea of ”Almost injective modules”. Let , be two modules. is said Almost -Injective, if for any homomorphism ,, either extends to a homomorphism or there exist a decomposition with and a homomorphism such that for any , where is a projection with kernel . A module that is almost -injective, is called an almost self-injective module. A ring is called right almost self-injective if it is almost self-injective as a right module over itself.
