  We calculate presupernova evolutions and supernova explosions of massive
stars (M=13-25 Mo) for various metallicities. We find the following
characteristic abundance patterns of nucleosynthesis in the metal-free (Pop
III) stars. (1) The alpha-nuclei (from C to Zn) are more efficiently produced
than other isotopes, and the abundance pattern of alpha-nuclei can be similar
to the solar abundance. In particular, near solar ratios of alpha elements/Fe
might be a signature of Pop III which could produce a large amount of Fe. (2)
The abundance ratios of odd Z to even Z elements such as Na/Mg and Al/Mg become
smaller for lower metallicity. However, these ratios almost saturate below Z <~
10^{-5}, and [Na, Al/Mg] ~ - 1 for Pop III and low metal Pop II
nucleosynthesis. This result is consistent with abundance pattern of metal poor
stars, in which these ratios also saturate around -1. We suggest that these
stars with the lowest [Na/Mg] or [Al/Mg] may contain the abundance pattern of
Pop III nucleosynthesis. (3) Metal poor stars show interesting trends in the
ratios of [Cr, Mn, Co/Fe]. We discuss that these trends are not explained by
the differences in metallicity, but by the relative thickness between the
complete and the incomplete Si burning layers. Large [Co/Fe] and small [Cr,
Mn/Fe] values found in the observations are explained if mass cut is deep or if
matter is ejected from complete Si burning layer in a form of a jet or bullets.
(4) We also find that primary ^{14}N production occurs in the massive Pop III
stars, because these stars have radiative H-rich envelopes so that the
convective layer in the He-shell burning region can reach the H-rich region.
