Abstract: Renormalizations, which sum classes of diagrams to all orders in perturbation theory, are applied to the electron propagator. The separation of relaxation and correlation self-energy diagrams enables the construction of electron propagators that include relaxation contributions to all orders. Correlation self-energies are obtained in second order, third order, and in the diagonal 2p-h Tamm-Dancoff approximation, which is also a renormalization. These propagators are applied to the electron binding energies of CN, NFL, PFL and Cl2. An alternative propagator renormalization through the transition operator method reference state is applied to the electron binding energies of Ne, FLO, Ne, H2O, NH2, and CN. The anti symmetrized geminal power wavefunction, which is the form of the consistent ground state of the random phase approximation of the polarization propagator, is variationally optimized for the LiH groundstate potential curve. Random phase approximation polarization propagator calculations yield excitation energies. Physical concepts suggested by these theories are discussed. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Propagator Calculations on Molecular Ionization and Excitation Processes" by Joseph Vincent Ortiz, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.