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During the last few years, a number of exceptional core-collapse supernovae(SNe) have been discovered. Their kinetic energy of the explosions are largerby more than an order of magnitude than the typical values for this type ofSNe, so that these SNe have been called `Hypernovae'. We first describe how thebasic properties of hypernovae can be derived from observations and modeling.These hypernovae seem to come from rather massive stars, thus forming blackholes. On the other hand, there are some examples of massive SNe with only asmall kinetic energy. We suggest that stars with non-rotating black holes arelikely to collapse "quietly" ejecting a small amount of heavy elements (Faintsupernovae). In contrast, stars with rotating black holes are likely to giverise to very energetic supernovae (Hypernovae). We present distinctnucleosynthesis 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 ischaracterized by a large amount of fall-back. We show that the abundancepattern of the most Fe deficient star, HE0107-5240, and other extremelymetal-poor carbon-rich stars are in good accord with those ofblack-hole-forming supernovae, but not pair-instability supernovae. Thissuggests that black-hole-forming supernovae made important contributions to theearly Galactic (and cosmic) chemical evolution.Comment: 49 pages, to be published in "Stellar Collapse" (Astrophysics and  Space Science; Kluwer) ed. C. L. Fryer (2003

Hypernovae and Other Black-Hole-Forming Supernovae