We review the Floquet theory of linear differential equations with periodic
coefficients and discuss its applications to neutrino oscillations in matt
er of periodically varying density. In particular, We consider a parametric
resonance in neutrino oscillations that is possible in such media and disc
uss its implications for the oscillations of neutrinos traversing the faith
and passing through the Earth's core. (C) 2001 MAIK "Nauka/Interperiodica"
.