  The collapse of dense cores with different metallicities is studied by
hydrodynamical calculations coupled with detailed chemical and radiative
processes. For this purpose, we construct a simple chemical network with
non-equilibrium reactions among 15 chemical species, which reproduces the
abundance of important molecular coolants by more detailed network very well.
The evolution is followed until the formation of a hydrostatic protostar at the
center. In a lower-metallicity gas cloud, the temperature during the collapse
remains high owing to less efficient cooling. Using the temperature evolution
at the center as a function the density, we discuss the possibility of
fragmentation during the dust-cooling phase. The critical metallicity for the
fragmentation is 10^{-5}Z_sun assuming moderate elongation of the cloud cores
at the onset of this phase. From the density and velocity distributions at the
time of protostar formation, we evaluate the mass accretion rate in the
subsequent accretion phase. Using these accretion rates, we also calculate the
evolution of the protostars under the assumption of stationary accretion flow.
Finally, we discuss possible suppression of fragmentation by heating of the
ambient gas by protostellar radiation, which is considered important in the
contemporary star formation. We argue that it is negligible for <10^{-2}Zsun.
