Abstrac: Let A be a banach algebra. In this thesis we first define left approximate identity, right approximate identity and approximate identity, then define left and right approximate unit. We survey exist of approximate identity in banach algebra. We establish the connection between the existence of a bounded approximate identity and the factorization theory and show by example that the converse is false, i.e we give an example of banach algebra all of whose elements can be factored, but wich has no bounded left or right approximate identity. Then express application of this theorem. Also, We survey exist of approximate identity in group algebra like L p (G), L 1 (G).