The concept of resolvability and affine resolvability was generalized to $\mu$-resolvability and affine $\mu$-resolvability by Shrikhande and Raghavarao (1964). In this paper, a representation of parameters of an affine $\mu$-resolvable BIB design is given and necessary conditions for the existence of this design are derived. Some methods of constructing (affine) $\mu$-resolvable BIB designs are given and some inequalities for these designs are obtained. Finally, some information on the block structure of $\mu$-resolvable BIB designs is provided.