This M.S.c. thesis is based on the following papers • Goodner, D. B.,“Projections in normed linear spaces”,Trans. Amer. Math. Soc., Vol. ??, pp. ???-???,????. • Graven, A. W. M.,“Injective and projective banach modules”, Nederl. Akad. Wetensch. Indag. Math., Vol. ??, No. ?, pp. ???-???,????. One of the most important and primitive theorems in functional analysis is, Hahn-Banach theorem. In this thesis, we examine one of the results the Hahn-Banach theorem which is expressed as follows: If Z is a suace of a normed linear space X on field C and T is a bounded linear functional on Z then T can be extended to a bounded linear functional T ? on X such that for every x ? Z, ? T ?Z = ? T ? ?X; T(x) = T ?(x). In fact, in Hahn-Bananch theorem, Banach space C has a fundamental role. By changing Banach space C, with other Banach space, we arrive to the injective space.