  Phenomenology of neutrino oscillations in vacuum and in cosmological plasma
is considered. Neutrino oscillations in vacuum are usually described in plane
wave approximation. In this formalism there is an ambiguity if one should
assume $\delta p =0$ and correspondingly $\delta E\neq 0$ or vice versa $\delta
E =0$ and $\delta p \neq 0$, or some other condition. We will use the standard
set of quantum field theory rules and show that the theoretical description is
unambiguous and that the state of oscillating neutrinos is determined by the
conditions of their registration. The wave packet formalism is a natural result
of such an approach. Oscillating neutrinos in cosmological plasma cannot be
described in terms of wave function because of a fast loss of coherence due to
elastic or inelastic scattering, so that one should use the density matrix
formalism. Kinetic equations for the density matrix of oscillating neutrinos
are derived. Numerical and semi-analytical solutions of the equations are
examined. In particular, a possibility of amplification of cosmological lepton
asymmetry in the sector of active neutrinos mixed to sterile ones is critically
discussed.
