A review of the IMF

The present-day mass function (PDMF) of field stars in the solar neighborhood is discussed. Major uncertainties in the derivation exist, in particular the luminosity-mass relation and the bolometric corrections. Consequently, it is not clear whether the PDMF turns over at very low masses (M<0.3 MSun), and the slope at the high-mass end (M>10 MSun) is more uncertain than usually assumed. The reality of two features in the PDMF (at M∼1.2 MSun and M∼3 MSun) is an open question. Next, the concept of a bimodal IMF is critically examined. Both Guesten and Mezger's (1983) and Larson's (1986) bimodal models may run into problems. If the effects of high-mass stars prevent low-mass stars from forming, the term ''biassed IMF'' is a better description of the situation than ''bimodal IMF''. The IMF is probably not universal; reported IMF variations in open clusters and globular clusters are unlikely to be spurious. Finally the physics of the IMF is discussed. The fact that the mass of a star in the making depends on many random-valued (multiplicative) input parameters suggests a stochastic rather than a deterministic approach to the origin of IMF. (author). 6 figs., 72 refs