  We present a formalism for precise description of oscillation phenomena in
matter at high energies or high densities, V > \Delta m^2/2E, where V is the
matter-induced potential of neutrinos. The accuracy of the approximation is
determined by the quantity \sin^2 2\theta_m \Delta V/2\pi V, where \theta_m is
the mixing angle in matter and \Delta V is a typical change of the potential
over the oscillation length (l \sim 2\pi/V). We derive simple and physically
transparent formulas for the oscillation probabilities, which are valid for
arbitrary matter density profiles. They can be applied to oscillations of high
energy (E > 10 GeV) accelerator, atmospheric and cosmic neutrinos in the matter
of the Earth, substantially simplifying numerical calculations and providing an
insight into the physics of neutrino oscillations in matter. The effect of
parametric enhancement of the oscillations of high energy neutrinos is
considered. Future high statistics experiments can provide an unambiguous
evidence for this effect.
