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We construct a new perturbative framework to describe neutrino oscillation inmatter with the unique expansion parameter \epsilon, which is defined as \Deltam^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 themaximally compact expressions of the oscillation probabilities in matter toorder \epsilon in the form akin to those in vacuum. This feature allowsimmediate physical interpretation of the formulas, and facilitatesunderstanding of physics of neutrino oscillations in matter. Moreover, quiterecently, we have shown that our three-flavor oscillation probabilitiesP(\nu_\alpha \rightarrow \nu_\beta) in all channels can be expressed in theform of universal functions of L/E. The \nu_e disappearance oscillationprobability P(\nu_e \rightarrow \nu_e) has a special property that it can bewritten as the two-flavor form which depends on the single frequency. This talkis based on the collaborating work with Stephen Parke [1].

Flavor-Universal Form of Neutrino Oscillation Probabilities in Matter