  We review current theories for the origin of the Stellar Initial Mass
Function (IMF) with particular focus on the extent to which the IMF can be
considered universal across various environments. To place the issue in an
observational context, we summarize the techniques used to determine the IMF
for different stellar populations, the uncertainties affecting the results, and
the evidence for systematic departures from universality under extreme
circumstances. We next consider theories for the formation of prestellar cores
by turbulent fragmentation and the possible impact of various thermal,
hydrodynamic and magneto-hydrodynamic instabilities. We address the conversion
of prestellar cores into stars and evaluate the roles played by different
processes: competitive accretion, dynamical fragmentation, ejection and
starvation, filament fragmentation and filamentary accretion flows, disk
formation and fragmentation, critical scales imposed by thermodynamics, and
magnetic braking. We present explanations for the characteristic shapes of the
Present-Day Prestellar Core Mass Function and the IMF and consider what
significance can be attached to their apparent similarity. Substantial
computational advances have occurred in recent years, and we review the
numerical simulations that have been performed to predict the IMF directly and
discuss the influence of dynamics, time-dependent phenomena, and initial
conditions.
