  We investigate the thermal and dynamical evolution of primordial gas clouds
in the universe after decoupling. Comparing the time-scale of dynamical
evolution with that of fragmentation, we can estimate the typical fragmentation
scale. We propose the following scenario of the formation process of first
luminous objects consisting of large number stars. First, by pancake collapse
of the overdensity regions in the expanding universe or collision between
clouds in potential wells, quasi-plane shocks form. If the shock-heated
temperature is higher than about $10^4$ K, the postshock gas cools down to
several hundred K by \Hbun line cooling, and the shock-compressed layer
fragments into filamentary clouds. The filamentary cloud collapses dynamically
once more and fragments into cloud cores. Finally, a primordial star forms in a
cloud core. We show that the minimum mass of the first star is essentially
determined by the Chandrasekhar mass. Also, we investigate the dynamical
collapse of cloud cores by numerical simulation and show that the evolution
paths of the central regions of the cores depend only very weakly on the total
core mass. After mass accretion, a massive star may be formed in a core, since
the estimated mass accretion rate is very large. In such a case, it may be
possible for many massive stars form almost simultaneously. Then the clouds can
be luminous objects. On the other hand, if the shock-heated temperature is
lower, effective star formation is delayed significantly.
