  Stars form by gravoturbulent fragmentation of interstellar gas clouds. The
supersonic turbulence ubiquitously observed in Galactic molecular gas generates
strong density fluctuations with gravity taking over in the densest and most
massive regions. Collapse sets in to build up stars and star clusters.
  Turbulence plays a dual role. On global scales it provides support, while at
the same time it can promote local collapse. Stellar birth is thus intimately
linked to the dynamic behavior of parental gas clouds, which governs when and
where protostellar cores form, and how they contract and grow in mass via
accretion from the surrounding cloud material to build up stars. The equation
of state plays a pivotal role in the fragmentation process. Under typical cloud
conditions, massive stars form as part of dense clusters following the "normal"
mass function observed, e.g. in the solar neighborhood. However, for gas with
an effective polytropic index greater than unity star formation becomes biased
towards isolated massive stars. This is relevant for understanding the
properties of zero-metallicity stars (Population III) or stars that form under
extreme environmental conditions like in the Galactic center or in luminous
starbursts.
