  In this paper I should like to present {\bf {{the four new effects}}} in
neutrino oscillations that have been recently investigated in my research group
at the Department of Theoretical Physics of the Moscow State University. Due to
the fact that these studies were stimulated by our previous research of
neutrino interactions in the presence of magnetic fields, and also because the
year 2004 commemorates the 40th years jubilee since the the first paper on the
neutrino interaction in a magnetic field was published, a short review on the
first papers dedicated to the problem of neutrinos in magnetic fields, and also
on the recent results in this field, prefaces (Section 1) the discussion on
{\bf the new effects} in neutrino oscillations. Section 2 is devoted to our
recent studies of the electromagnetic properties of a {\it massive} neutrino,
including the neutrino magnetic moment for different values of neutrino mass.
In Section 3 we discuss {\it \bf the four new effects} in neutrino spin and
flavour oscillations in different background environments.
