The T2K Experiment is a long-baseline accelerator neutrino oscillation experiment, whose primary aim is to look for νe appearance in a νμ beam. A predominantly νμ beam is produced at J-PARC in Tokai on the east coast of Japan, and neutrino interactions are measured both by a near detector complex, 280 m from the neutrino production target,and by a large water Cerenkov detector, Super-Kamiokande, 295 km away. This thesis is concerned with oscillations νμ → νe, within both a standard three neutrino model and a model in which there is one additional sterile neutrino. By looking at νe appearance over the T2K baseline, this thesis looks for oscil- lations involving one additional sterile neutrino. A region of the short baseline neutrino oscillation parameter space favoured by other experiments is excluded at 3σ. The ND280 is also used to search for νe appearance over a short baseline. A νe selection is developed, and limits on the short baseline oscillation parameter space are set. Sensitivity predictions are also made for future T2K running. The T2K ND280 is interesting for this work since the detector technology is different to that of other experiments that have seen indications of short baseline electron-neutrino appearance. In the standard three-flavour neutrino oscillation picture, a combined analy- sis of the electron-neutrino appearance results of T2K and another long-baseline accelerator neutrino experiment, MINOS, is presented. Combining the two re- sults with the Feldman-Cousins method results in sin2 2θ13 = 0 being excluded at 2.7σ, assuming the normal neutrino mass hierarchy.</p
