  We present recent advances in theoretical studies of the formation and
evolution of dust in primordial supernovae (SNe) that are considered to be the
main sources of dust in the early universe. Being combined with the results of
calculations of dust formation in the ejecta of Population III SNe, the
investigations of the evolution of newly formed dust within supernova remnants
(SNRs) show that smaller grains are predominantly destroyed by sputtering in
the shocked gas, while larger grains are injected into the ambient medium. The
mass of dust grains surviving the destruction in SNRs reaches up to 0.1--15
$M_\odot$, which is high enough to account for the content of dust observed for
the host galaxies of quasars at $z > 5$. In addition, the transport of dust
formed in the ejecta causes the formation of low-mass stars in the dense shell
of primordial SNRs and affects the elemental composition of those stars. We
also show that the flat extinction curve is expected in the high-redshift
universe where SNe are the possible sources of dust.
