  We construct a new perturbative framework to describe neutrino oscillation in
matter with the unique expansion parameter \epsilon, which is defined as \Delta
m^2_{21} / \Delta m^2_{ren} with the renormalized atmospheric \Delta m^2_{ren}
\equiv \Delta m^2_{31} - s^2_{12} \Delta m^2_{21}. It allows us to derive the
maximally compact expressions of the oscillation probabilities in matter to
order \epsilon in the form akin to those in vacuum. This feature allows
immediate physical interpretation of the formulas, and facilitates
understanding of physics of neutrino oscillations in matter. Moreover, quite
recently, we have shown that our three-flavor oscillation probabilities
P(\nu_\alpha \rightarrow \nu_\beta) in all channels can be expressed in the
form of universal functions of L/E. The \nu_e disappearance oscillation
probability P(\nu_e \rightarrow \nu_e) has a special property that it can be
written as the two-flavor form which depends on the single frequency. This talk
is based on the collaborating work with Stephen Parke [1].
