In this dissertation atmospheric neutrino data from the 50 kiloton water-Cherenkov detector, Super-Kamiokande, are studied in the context of neutrino oscillations. Data presented here are taken from the 1489-day SK-I and 803-day SK-II exposures. Super-Kamiokande's atmospheric neutrino sample exhibits a zenith angle dependent deficit of vmu interactions which is well explained by maximal two-flavor vmu double arrow vgamma oscillations. This analysis extends the two-flavor framework to include all active neutrino flavors and searches for sub-dominant oscillation effects in the oscillations of atmospheric neutrinos. If the last unknown mixing angle, theta13, is non-zero there is enhancement (suppression) of the vmu to ve three-flavor oscillation probability in matter for several GeV neutrinos with long baselines under the normal (inverted) mass hierarchy. At Super-Kamiokande this effect would manifest itself as an increase in the high energy ve event rate coming from below the detector. Searching the SK-I, SK-II and their combined data finds no evidence of a rate excess and yields a best fit to theta13 of zero assuming either hierarchy. This extended analysis remains consistent with the current knowledge of two-flavor atmospheric mixing finding best fit values sin2theta23 equals 0.5 and deltam2 equals 2.6x10minus3eV2. No preference for either the normal or inverted mass hierarchy is found in the data.