  A new type of electromagnetic radiation by a neutrino with non-zero magnetic
(and/or electric) moment moving in background matter and electromagnetic field
is considered. This radiation originates from the quantum spin flip transitions
and we have named it as "spin light of neutrino"($SL\nu$). The neutrino
initially unpolarized beam (equal mixture of $\nu_{L}$ and $\nu_{R}$) can be
converted to the totally polarized beam composed of only $\nu_{R}$ by the
neutrino spin light in matter and electromagnetic fields. The quasi-classical
theory of this radiation is developed on the basis of the generalized
Bargmann-Michel-Telegdi equation. The considered radiation is important for
environments with high effective densities, $n$, because the total radiation
power is proportional to $n^{4}$. The spin light of neutrino, in contrast to
the Cherenkov or transition radiation of neutrino in matter, does not vanish in
the case of the refractive index of matter is equal to unit. The specific
features of this new radiation are: (i) the total power of the radiation is
proportional to $\gamma ^{4}$, and (ii) the radiation is beamed within a small
angle $\delta \theta \sim \gamma^{-1}$, where $\gamma$ is the neutrino Lorentz
factor. Applications of this new type of neutrino radiation to astrophysics, in
particular to gamma-ray bursts, and the early universe should be important.
