<p> </p> <ol> <li>This dissertation investigates the thermodynamics and transport of vacancies and interstitials of oxygen (O) and thorium (Th) in thorium dioxide (ThO₂) with varying charge states from neutral to maximum, with respect to temperature and oxygen pressure. The study also explores the impact of varying fractions of uranium (U) as a cation (<em>y</em>) on the defect disorder in mixed oxide fuels (Th_1-<em>y</em>U_<em>y</em>O₂). Understanding the properties of point defects in these oxides lays a strong foundation, as defects influence the properties of bulk materials, such as thermal transport. To accomplish the stated objectives of this dissertation, the research is structured into three sections that employ first principles density functional theory (DFT) and phonon calculations. The first section focuses on the structure, internal energy of formation, and vibrational entropy of point defects in ThO₂. The results demonstrate that defect energetics increase with an increase in defect charge for O interstitials and Th vacancies, while the opposite is true for O vacancies and Th interstitials. The lowest internal energy of formation shifts from O vacancies of charge 2+ to O interstitials and Th vacancies at various temperature ranges of 0 to 600 K, 600 to 1300 K, and 1300 to 2000 K. The second section develops a model to calculate the defect disorder and off-stoichiometry in ThO_{2±<em>x</em>} and Th_1-<em>y</em>U_<em>y</em>O_{2±<em>x</em>}. The model shows that ThO₂ exists mainly as a hypo-stoichiometric oxide between 1200 K to 2900 K for oxygen pressures ranging from 10^-30 to 10 atm, with O defects dominating this off-stoichiometric regime. The addition of U increases the thermodynamic window over which Th_1-<em>y</em>U_<em>y</em>O2 is hyper-stoichiometric, with O vacancies dominating in the hypo-stoichiometric regime, and cation vacancies and O interstitials dominating at low and high temperatures, respectively. Specifically, at low U content and low temperatures, U vacancies dominate hyper-stoichiometry, while at high U content and low temperatures, Th vacancies are dominant. This research facilitates the comprehension of the intricate changes in structural and defect equilibria that take place during nuclear fuel irradiation, where the fuel is not in a stoichiometric condition. The third section of the dissertation investigates migration barriers and diffusivities of defects and of O and Th in ThO₂. Results indicate that the migration energy of a point defect is dependent on its charge state. The average diffusivity of O vacancies exceeds that of O interstitials, while the similar is true for Th vacancies and Th interstitials above 1650 K. The self-diffusion coefficient of O and Th increases with temperature and is influenced by oxygen pressure, showing a close agreement with experimental and molecular-dynamics-based computational data. At 1500 K, the self-diffusivity of O and Th in ThO2 is 7.47 x 10^-16 m²s^-1 and 4.48 x 10^-23 m²s^-1 , respectively, while at 2500 K, the values increase to 1.06 x 10^-12 m²s^-1  and 2.28 x 10^-17 m²s^-1 , respectively. The chemical diffusion coefficients of defects decrease initially and then plateau as the hypo-stoichiometry in the oxide increases. These findings serve as a fundamental framework for understanding the diffusion-controlled processes of defects, which affect the radiation tolerance and microstructural evolution of ThO₂ as a nuclear fuel.  </li> </ol>