  During the last few years, a number of exceptional core-collapse supernovae
(SNe) have been discovered. Their kinetic energy of the explosions are larger
by more than an order of magnitude than the typical values for this type of
SNe, so that these SNe have been called `Hypernovae'. We first describe how the
basic properties of hypernovae can be derived from observations and modeling.
These hypernovae seem to come from rather massive stars, thus forming black
holes. On the other hand, there are some examples of massive SNe with only a
small kinetic energy. We suggest that stars with non-rotating black holes are
likely to collapse "quietly" ejecting a small amount of heavy elements (Faint
supernovae). In contrast, stars with rotating black holes are likely to give
rise to very energetic supernovae (Hypernovae). We present distinct
nucleosynthesis features of these two types of "black-hole-forming" supernovae.
Hypernova nucleosynthesis is characterized by larger abundance ratios
(Zn,Co,V,Ti)/Fe and smaller (Mn,Cr)/Fe. Nucleosynthesis in Faint supernovae is
characterized by a large amount of fall-back. We show that the abundance
pattern of the most Fe deficient star, HE0107-5240, and other extremely
metal-poor carbon-rich stars are in good accord with those of
black-hole-forming supernovae, but not pair-instability supernovae. This
suggests that black-hole-forming supernovae made important contributions to the
early Galactic (and cosmic) chemical evolution.
