The observation of neutrino oscillations (neutrino changing from one flavor to another) has provided compelling evidence that the neutrinos have non-zero masses and that leptons mix, which is not part of the original Standard Model of particle physics. The theoretical framework that describes neutrino oscillation involves two mass scales (∆m 2 atm and ∆m 2 sol ), three mixing angles (θ 12 , θ 23 , and θ 13 ) and one CP violating phase (δ CP ). Both mass scales and two of the mixing angles (θ 12 and θ 23 ) have been measured by many neutrino experiments. The mixing angle θ 13 , which is believed to be very small, remains unknown. The current best limit on θ 13 comes from the CHOOZ experiment: θ 13 < 11• at 90% C.L. at the atmospheric mass scale. δ CP is also unknown today.MINOS, the Main Injector Neutrino Oscillation Search, is a long baseline neutrino experiment based at Fermi National Accelerator Laboratory. The experiment uses a muon neutrino beam, which is measured 1 km downstream from its origin in the Near Detector at Fermilab and then 735 km later in the Far Detector at the Soudan mine. By comparing these two measurements, MINOS can obtain parameters in the atmospheric sector of neutrino oscillations. MINOS has published results on the precise measurement of ∆m 2 atm and θ 23 through the disappearance of muon neutrinos in the Far Detector and on a search for sterile neutrinos by looking for a deficit in the number of neutral current interactions seen in the Far Detector. MINOS also has the potential to improve the limit on the neutrino mixing angle θ 13 or make the first v measurement of its value by searching for an electron neutrino appearance signal in the Far Detector. This is the focus of the study presented in this thesis.We developed a neural network based algorithm to distinguish the electron neutrino signal from background. The most important part of this measurement is the background estimation, which is done through extrapolation. The number of background events is measured at the Near Detector, then extrapolated to the Far Detector. Since different background sources extrapolate differently, some knowledge about the relative contribution from different background sources is necessary. We developed a method that can be used to obtain relative contributions of various background sources from comparison of background rates in the horn-on and horn-off configurations. We also described our effort to improve two aspects of the Monte Carlo simulation which are very important for the ν e appearance analysis: one is the hadronization model in the neutrino-nucleon interactions, the other is the modeling of PMT crosstalk. We performed a blind analysis and examined several sidebands before looking at the signal region. After we opened the box, we observed a 1.4 σ excess of ν e -like events in the Far Detector compared with the number of predicted background events. The excess is well within the statistical fluctuation of the background events. If we interpret the excess as a ν e signal from ν µ → ν...