Projective and injective dimensions of modules. Global dimension of the ring. Functors Extn without projective and injective resolutions. Proper classes of short exact sequences. Examples. Operations over proper classes. Functors Extn with respect to a proper class. Projective and injective objects with respect to a proper class. Projectively and inlectively generated proper classes. Coprojective and coinjective objects. Coprojectively and coinlectively generated proper classes. Projective, injective and global dimensions with respect to proper classes.