A strong case has been made by several experiments that neutrinos oscillate, although important questions remain as to the mechanisms and precise values of the parameters. In the standard picture, two parameters describe the nature of how the neutrinos oscillate: the mass-squared difference between states and the mixing angle. The purpose of this thesis is to use data from the MINOS experiment to precisely measure the parameters associated with oscillations first observed in studies of atmospheric neutrinos. MINOS utilizes two similar detectors to observe the oscillatory nature of neutrinos. The Near Detector, located 1 km from the source, observes the unoscillated energy spectrum while the Far Detector, located 735 km away, is positioned to see the oscillation signal. Using the data in the Near Detector, a prediction of the expected neutrino spectrum at the Far Detector assuming no oscillations is made. By comparing this prediction with the MINOS data, the atmospheric mixing parameters are measured to be [special characters omitted]×10^-3 eV² and sin²(2&thetas; ₃₂) =[special characters omitted] (> 0.90 at 90% confidence level).