: In this theses, for Banach algebra A and non-zero character ? o A, we give some necessary and sufficient condition for left? -contractibility of A as well as several hereditary properties. We also study relations between homological properties of some Banach left A-modules, left ?-contractibility and right ?-amenability of A. We characterize left character contractibility of various Banach algebras related to locally compact groups. Finally, we investigate some homological properties of Banach modules over group algebras related to locally compact groups.