  The first stars are assumed to be predominantly massive. Although, due to the
low initial abundances of heavy elements the line-driven stellar winds are
supposed to be inefficient in the first stars, these stars may loose a
significant amount of their initial mass by other mechanisms.
  In this work, we study the evolution with a prescribed mass loss rate of very
massive, galactic and pregalactic, Population III stars, with initial
metallicities $Z=10^{-6}$ and $Z=10^{-9}$, respectively, and initial masses
100, 120, 150, 200, and 250$\,M_{\odot}$ during the hydrogen and helium burning
phases.
  The evolution of these stars depends on their initial mass, metallicity and
the mass loss rate. Low metallicity stars are hotter, compact and luminous, and
they are shifted to the blue upper part in the Hertzprung-Russell diagram. With
mass loss these stars provide an efficient mixing of nucleosynthetic products,
and depending on the He-core mass their final fate could be either
pair-instability supernovae or energetic hypernovae. These stars contributed to
the reionization of the universe and its enrichment with heavy elements, which
influences the subsequent star formation properties.
