In this work we try to understand the phenomena of neutrino oscillations, and use this to obtain a more precise description of the atmospheric neutrino data. The two neutrino oscillation mechanism solves the problem of the up-down muon neutrino asymmetry successfully. Our main motivation is to describe the excess of events of electron-neutrino type found in the SuperKamiokande results at low energies when compared with the predictions of the two-generation neutrino oscillation. To do this we generalize the oscillation model from two to three neutrino flavors, opening the possibility of oscillation between electron neutrino type and the others. Then we obtain a semi-analytic solution of the three flavors problem using the neutrino phenomenological limits on oscillation parameters, squared masses differences and mixing angles. For this we must take into account matter effects on the electronic neutrino when it cross the Earth and has its oscillation pattern changed.