S. Offner (Yale University, United States),
P. Clark (Heidelberg University, ITA, Germany),
P. Hennebelle (Observatoire de Paris, LERMA, Paris, France),
N. Bastian (Liverpool John Moores University, United Kingdom),
M. Bate (University of Exeter, United Kingdom),
P. Hopkins (California Institute of Technology, Department of Astronomy, United States),
E. Moraux (Institut de Planetologie et d'Astrophysique de Grenoble (IPAG), France),
A. Whitworth (Cardiff University, Physics & Astronomy, United Kingdom)

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, disc 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.

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