Let (A, \\Vert. \\Vert) be a B anach algebra and X a locally compact Hausdorff space. Consider the Banach algebra C _{?} (X,A) of continuous functions on X into A vanishing at infinity; this is endowed with pointwise defined operation s and the supremum norm. In this thesis deals with Segal algebra, norm irregularity and approximate identity in C _{?} (X,A) . Actually, these notions are deduced from the corresponding properties of A . Segal algebras were first introduced in the context of group algebras in the late ????s by Hans Reiter [??], and were later given an definition by Burnham [??].