  We report strongly correlated electronic band structure calculations of the
recently discovered double-layer high-temperature superconductor
La$_3$Ni$_2$O$_7$ under pressure. Our calculations reveal dual nature of Ni-$d$
electrons with almost localized $d_{z^2}$ orbitals due to onsite Coulomb
repulsion and very flat hybridization bands of Ni-$d_{x^2-y^2}$ and
Ni-$d_{z^2}$ quasiparticles near the Fermi energy. We find that the
quasiparticle effective mass are greatly enhanced by the Hund's rule coupling
and their lifetimes are inversely proportional to the temperature, which
explains the experimentally observed strange metal behavior in the normal
state. We also find strong antiferromagnetic spin correlations of Ni-$d$
electrons, which may provide the pairing force of quasiparticles for the
high-temperature superconductivity. These give a potential explanation of two
key observations in experiment and connect the superconducting
La$_3$Ni$_2$O$_7$ with cuprate high-temperature superconductors. The presence
of flat bands and the interplay of orbital-selective Mott, Hund, and Kondo
physics make La$_3$Ni$_2$O$_7$ a unique platform for exploring rich emergent
quantum many-body phenomena in the future.
