  We give a perturbation theory of neutrino oscillation in the Earth. The
perturbation theory is valid for neutrinos with energy $E \gsim 0.5$ GeV. It is
formulated using trajectory dependent average potential. Non-adiabatic
contributions are included as the first order effects in the perturbation
theory. We analyze neutrino oscillation with standard matter effect and with
non-standard matter effect. In a three flavor analysis we show that the
perturbation theory gives a precise description of neutrino conversion in the
Earth. Effect of the Earth matter is substantially simplified in this
formulation.
