First Stars: Their Supernova Explosions and Connections to Extremely Iron-Poor Stars*

First stars in the universe must have played crucial roles in the evolution of early universe, yet their nature has not been well-understood.  I will present possible theoretical models of  first stars, i.e., their evolution with mass accretion, explosions as first supernovae, and explosive nucleosynthesis.  I will show how the comparison between the nucleosynthesis yields and the peculiar abundance patterns observed in extremely iron-poor stars can constrain the properties (mass function, explosion energy, asphericity, etc.) of first stars and first supernovae.