In the thesis the properties of projective and injective Banach modules are investigated. Also, the approach of Ghahramani and Loy is extended to the setting of Banach modules by showing that projective and injective Banach modules can be characterized in approximate terms. As a corollary, the approximate characterization of biprojective, biflat and amenable Banach algebras are obtained. In particular, it is proved that a uniformly approximately amenable Banach algebra is automatically amenable, and an alternative proof of this result of Ghahramani and Loy obtained.Finally, we show that the proof of Corollary 3.4 of the paper is not correct and give a new proof of this result, and also we generalize this result.
