Probing the 'MeV Gap': Discovery and Characterization of Persistent and Transient MeV-GeV Gamma-ray Sources with the Fermi Large Area Telescoope

The MeV Gap is a moniker for the energy regime E~0.1-100 MeV that has lacked sensitive observations for the last 20 years. This is not out of scientific disinterest, but observational challenges. The only instrument currently available to make observations in the MeV Gap is the Fermi Large Area Telescope (LAT). For the first time ever, Fermi-LAT has been leveraged to push its observational capabilities to its absolute lower energy limit to end this 20-year observational gap. Observing the MeV sky is imperative for identifying some of the most luminous galaxies in the Universe known as blazars. The brightest blazars have emission that is dominated by MeV energies. Powered by supermassive black hole accretion, MeV blazars are found at high redshift, therefore their identification can help to understand the presence of supermassive black holes very early in the Universe as well as being sources of extragalactic neutrinos, whose origin is still not precisely known. Furthermore, Galactic gamma-ray sources, and other gamma-ray objects without a precise origin have neglected study. This dissertation identified 450 MeV-bright objects, 62 which are newly discovered gamma-ray emitters. Additionally, a historical investigation identified the demographic and rate of Galactic gamma-ray flaring sources which can be used to constrain theoretical models on the evolution of objects such as binaries and pulsar wind nebulae. Lastly, this work found 21 X-ray counterparts for unidentified gamma-ray sources and classified them with an improved machine learning algorithm, helping to streamline future classifications of unknown gamma-ray objects.