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.
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