  The evolution of collapsing metal free protostellar clouds is investigated
for various masses and initial conditions.
  We perform hydrodynamical calculations for spherically symmetric clouds
taking account of radiative transfer of the molecular hydrogen lines and the
continuum, as well as of chemistry of the molecular hydrogen.
  The collapse is found to proceed almost self-similarly like Larson-Penston
similarity solution.
  In the course of the collapse, efficient three-body processes transform
atomic hydrogen in an inner region of $\sim 1 M_{\sun}$ entirely into molecular
form.
  However, hydrogen in the outer part remains totally atomic although there is
an intervening transitional layer of several solar masses, where hydrogen is in
partially molecular form.
  No opaque transient core is formed although clouds become optically thick to
H$_{2}$ collision-induced absorption continuum, since H$_{2}$ dissociation
follows successively.
  When the central part of the cloud reaches stellar densities ($\sim
  10^{-2} {\rm g cm^{-3}}$), a very small hydrostatic core ($\sim
  5 \times 10^{-3} M_{\sun}$) is formed and subsequently grows in mass as the
ambient gas accretes onto it.
  The mass accretion rate is estimated to be $3.7 \times 10^{-2} M_{\sun}
  {\rm yr^{-1}} (M_{\ast}/M_{\sun})^{-0.37}$, where $M_{\ast}$ is instantaneous
mass of the central core, by using a similarity solution which reproduces the
evolution of the cloud before the core formation.
