We develop the approach to the problem of neutrino oscillations in a magnetic field introduced

in [1] and extend it to the case of three neutrino generations. The theoretical framework suitable

for computation of the Dirac neutrino spin, flavour and spin-flavour oscillations probabilities in

a magnetic field is given. The closed analytic expressions for the probabilities of oscillations

are obtained accounting for the normal and inverted hierarchies and the possible effect of CP

violation. In general, the neutrino oscillation probabilities exhibit quite a complicated

interplay of oscillations on the magnetic $\omega_B=\mu_{\nu} B$ and vacuum $\omega_{vac}=\frac{\Delta m^2_{ik}}{4p}$

frequencies. The obtained

results are of interest in applications to neutrino oscillations under the influence of extreme

astrophysical environments, for example peculiar to magnetars and supernovas, as well as in

studying neutrino propagation in interstellar magnetic fields (see [2]).