Over the past years observations of young and populous star clusters have shown that the stellar initial mass function (IMF) appears to be an invariant featureless Salpeter power law with an exponent ¼ 2:35 for stars more massive than a few M . A consensus has also emerged that most, if not all, stars form in stellar groups and star clusters and that the mass function of young star clusters in the solar neighborhood and in interacting galaxies can be described, over the mass range of a few 10 to 10 7 M , as a power law with an exponent % 2. These two results imply that galactic-field IMFs for early-type stars cannot, under any circumstances, be a Salpeter power law, but that they must have a steeper exponent, field e2:8. This has important consequences for the distribution of stellar remnants and for the chemodynamical and photometric evolution of galaxies.

The distribution of stellar masses that form together, the initial mass function (IMF), is one of the most important astrophysical distribution functions. The determination of the IMF is a very difficult problem because stellar masses cannot be measured directly and because observations usually cannot assess all stars in a population requiring elaborate bias corrections. Nevertheless, impressive advances have been achieved during the last decade, such that the shape of the IMF is reasonably well understood from low-mass brown dwarfs (BDs) to very massive stars. The case can be made for a rather universal form that can be well approximated by a two-part power-law function in the stellar regime. However, there exists a possible hint for a systematic variation with metallicity. From very elaborate observational surveys a picture is emerging according to which the binary properties of very-low-mass stars (VLMSs) and BDs may be fundamentally different from those of late-type stars implying the probable existence of a discontinuity in the IMF, but the surveys also appear to suggest the number of BDs per star to be independent of the physical conditions of current Galactic star formation. Star-burst clusters and thus globular cluster may, however, have a much larger abundance of BDs. Very recent advances have allowed the measurement of the physical upper stellar mass limit, which also appears to be disconcertingly robust to variations in metallicity. Furthermore, it now appears that star clusters are formed in a rather organised fashion from lowto high stellar masses, such that the most-massive stars just forming terminate further star-formation within the particular cluster. Populations formed from many star clusters, composite populations, would then have steeper IMFs (fewer massive stars per low-mass star) than the simple populations in the constituent clusters. A near invariant star-cluster mass function implies the maximal cluster mass to correlate with the galaxy-wide star-formation rate. This then leads to the result that the composite-stellar IMFs vary in dependence of galaxy type, with potentially dramatic implications for theories of galaxy formation and evolution.The simple and composite IMF 5 30 Dor cluster (R136) in the LMC, NGC 3603 in the MW, and the Arches cluster near the Galactic centre. The 30 Dor star-burst cluster (

We demonstrate that the mass of the most massive star in a cluster correlates non‐trivially with the cluster mass. A simple algorithm, according to which a cluster is filled up with stars that are chosen randomly from the standard initial mass function (IMF) but sorted with increasing mass, yields an excellent description of the observational data. Algorithms based on random sampling from the IMF without sorted adding are ruled out with a confidence larger than 0.9999. A physical explanation of this would be that a cluster forms by more‐massive stars being consecutively added until the resulting feedback energy suffices to revert cloud contraction and stops further star formation. This has important implications for composite populations. For example, 104 clusters of mass 102 M⊙ will not produce the same IMF as one cluster with a mass of 106 M⊙. It also supports the notion that the integrated galaxial stellar IMF (IGIMF) should be steeper than the stellar IMF and that it should vary with the star formation rate of a galaxy.