  The stellar initial mass function (IMF) in star clusters is reviewed.
Uncertainties in the observations are emphasized. We suggest there is a
distinct possibility that cluster IMFs vary systematically with density or
pressure. Dense clusters could have additional formation processes for massive
stars that are not present in low density regions, making the slope of the
upper mass IMF somewhat shallower in clusters. Observations of shallow IMFs in
some super star clusters and in elliptical galaxies are reviewed. We also
review mass segregation and the likelihood that peculiar IMFs, as in the Arches
cluster, result from segregation and stripping, rather than an intrinsically
different IMF. The theory of the IMF is reviewed in some detail. Several
problems introduced by the lack of a magnetic field in SPH simulations are
discussed. The universality of the IMF in simulations suggests that something
more fundamental than the physical details of a particular model is at work.
Hierarchical fragmentation by any of a variety of processes may be the dominant
cause of the power law slope. Physical differences from region to region may
make a slight difference in the slope and also appear in the low-mass turnover
point.
