In thi thesis, we introduce and study some notions of amenability of Banach algebras Such as approximate amenability and approximate weak amenability. We give a complete characterization for approximate amenability of a group algebras. We show that there exist approximately amenable Banach algebras which are not amenable (and of course weakly amenable). We finally show that for eny (with pointwise operation), is not amenable, however it is weakly amnenable.