Thesis: Sc. D., Massachusetts Institute of Technology, Department of Physics, 2020 "The following pages, 92-94, were not included in the original document submitted to the MIT Libraries. This is the most complete copy available"--Disclaimer page. Cataloged from PDF version of thesis. Supervised by Janet M. Conrad. Includes bibliographical references (pages 217-239). The IceCube Neutrino Observatory is capable of performing a unique search for sterile neutrinos through the exploitation of a matter enhanced resonant neutrino oscillation phenomena. As atmospheric muon neutrinos pass the dense material within the Earth, neutral current elastic forward scattering is predicted to induce a transition into a sterile state. This thesis presents two 3+1 sterile neutrino analyses by searching for spectral differences in the reconstructed energy and zenith direction of muon neutrino events, indicative of a transition into a sterile state. The first search probes the parameter space deltam²₄₁ and sin²(2theta₂₄) with relevant sensitivity to the global best fit region for a 3+1 sterile neutrino hypothesis. The second search performs a scan through sin²(2theta₂₄) and sin²(theta₃₄) in the oscillation averaged out region of high-deltam²₄₁ (theta²₄₁ >~ 10 eV²). The analyses are performed using an improved event selection, which was found to extract 305,891 well reconstructed muon neutrino events with a sample purity above 99.9%, from eight years of IceCube data. Novel simulation techniques, along with updated calibration, and a re-assessment of the systematic uncertainties are also discussed. The first analysis finds a best fit sterile hypothesis point at theta²₄₁ = 4.47eV² and sin²(theta₂₄ = 0.10, consistent with the no-sterile hypothesis at the 8% confidence level. The second analysis finds a best fit sterile hypothesis at sin²(theta₃₄ = 0.40, sin²(theta₃₄ =0.006, consistent with the null hypothesis at the 19% confidence level. by Spencer Nicholas Gaelan Axani. Sc. D. Sc. D. Massachusetts Institute of Technology, Department of Physics