  We investigate the indications of flavor oscillations that come from the
anomalous flavor composition of the atmospheric neutrino flux observed in some
underground experiments. We study the information coming from the
neutrino-induced $\mu$-like and $e$-like events both in the sub-GeV energy
range (Kamiokande, IMB, Fr{\'e}jus, and NUSEX experiments) and in the multi-GeV
energy range (Kamiokande experiment). First we analyze all the data in the
limits of pure $\nu_\mu\leftrightarrow\nu_\tau$ and
$\nu_\mu\leftrightarrow\nu_e$ oscillations. We obtain that
$\nu_\mu\leftrightarrow\nu_e$ oscillations provide a better fit, in particular
to the multi-GeV data. Then we perform a three-flavor analysis in the
hypothesis of dominance of one neutrino square mass difference, $m^2$, implying
that the neutrino mixing is parametrized by two angles,
$(\psi,\,\phi)\in[0,\,\pi/2]$. We explore the space $(m^2,\,\psi,\,\phi)$
exhaustively, and find the regions favored by the oscillation hypothesis. The
results are displayed in a form suited to the comparison with other flavor
oscillation searches at accelerator, reactor, and solar $\nu$ experiments. In
the analysis, we pay particular attention to the earth matter effects, to the
correlation of the uncertainties, and to the symmetry properties of the
oscillation probability.
