The recent discovery of a hyper metal-poor (HMP: -5 less than or similar to [Fe/H] less than or similar to -4) star have raised a challenging question if these HMP stars are first generation stars in the Universe. We argue that these HMP stars are the second generation stars being formed from gases which were chemically enriched by the first generation supernovae. The key to this solution is the very unusual abundance patterns of these HMP stars with important similarities and differences. We can reproduce these abundance features with the core-collapse "faint" supernova models which undergo extensive matter mixing and fallback during the explosion (mixing-fallback model). We also show that the abundance patterns of extremely metal-poor (EMP: -4 less than or similar to [Fe/H] less than or similar to -3) stars are well-reproduced by a 25 M-circle dot hypernova mixing-fallback model and those of very metal-poor (VMP: -3 less than or similar to [Fe/H] less than or similar to -2) stars are well-reproduced by a model integrated by Salpeter's initial mass function over 13 - 50 M-circle dot models.