Ultra-high energy (UHE) neutrinos are a promising messenger particle, and their discovery would be an important step towards understanding the universe at energies above 10^{18} eV. The ANtarctic Impulsive Transient Antenna (ANITA) is a NASA long duration balloon payload that aims to measure the UHE neutrino flux by detecting Askaryan radiation in the radio band from neutrinos interacting in the Antarctic ice. Previous ANITA flights have also demonstrated an ability to detect geomagnetically induced radio emission from UHE cosmic rays, both from emission beamed directly at the payload, and from emission that has been reflected off the Antarctic ice. In this thesis I present information about the fourth flight of ANITA, which took place during December of 2016. Contained within are details of the instument, the calibration procedures, the analysis, and finally, the results. In the neutrino channel of my analysis I find 1 candidate event on an expected background of 0.64^{+0.69}_{−0.45} events. While this is not a discovery, it does allow us to set the world leading limit at energies between 10^{19.5} eV and 10^{21} eV. In the cosmic ray and extensive air shower channel of my analysis, I find 28 events, 26 of which are likely candidates for normal cosmic ray induced extensive air showers. The remaining two events reconstruct to locations below the horizon, but lack the 180 degree phase inversion seen in reflected cosmic ray events.