The distribution of stellar masses that form in one star-formation event in a given volume of space is called the initial mass function (IMF). The IMF has been estimated from low-mass brown dwarfs to very massive stars. Combining IMF estimates for different populations in which the stars can be observed individually unveils an extraordinary uniformity of the IMF. This general insight appears to hold for populations including present-day star formation in small molecular clouds, rich and dense massive star-clusters forming in giant clouds, through to ancient and metal-poor exotic stellar populations that may be dominated by dark matter. This apparent universality of the IMF is a challenge for star formation theory because elementary considerations suggest that the IMF ought to systematically vary with star-forming conditions.The physics of star formation determines the conversion of gas to stars. The outcome of star formation are stars with a range of masses. Astrophysicists refer to the distribution of stellar masses as the stellar initial mass function. Together with the time-modulation of the star-formation rate, the IMF dictates the evolution and fate of galaxies and star clusters. The evolution of a stellar system is driven by the relative initial numbers of brown dwarfs (BDs, < ∼ 0.072 M ) that do not fuse H to He, very low-mass stars (0.072 − 0.5 M ), low-mass stars (0.5−1 M ), intermediate-mass stars (1−8 M ) and massive stars (m > 8 M ). Non-luminous BDs through to dim low-mass stars remove gas from the interstellar medium (ISM), lockingup an increasing amount of the mass of galaxies over cosmological time scales. Intermediate and luminous but short-lived massive stars expel a large fraction of their mass when they die and thereby enrich the ISM with elements heavier than H and He. They heat the ISM through radiation, outflows, winds and supernovae (1, 2). It is therefore of much importance to quantify the relative numbers of stars in different mass ranges and to find systematic variations of the 1