  In this chapter, we review some historical understanding and recent advances
on the Initial Mass Function (IMF) and the Core Mass Function (CMF), both in
terms of observations and theories. We focus mostly on star formation in
clustered environment since this is suggested by observations to be the
dominant mode of star formation. The statistical properties and the
fragmentation behaviour of turbulent gas is discussed, and we also discuss the
formation of binaries and small multiple systems.
