Nuclear reactions play a key role in the study of nuclei away from stability. Single-nucleon transfer reactions involving deuterons provide an exceptional tool to study the single-particle structure of nuclei. Theoretically, these reactions are attractive as they can be cast into a three-body problem composed of a neutron, proton, and the target nucleus.Optical potentials are a common ingredient in reactions studies. Traditionally, nucleon-nucleus optical potentials are made local for convenience. The effects of nonlocal potentials have historically been included approximately by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor. In this thesis, we have systematically investigated the effects of nonlocality on $(p,d)$ and $(d,p)$ transfer reactions, and the validity of the Perey correction factor. We implemented a method to solve the single channel nonlocal equation for both bound and scattering states. We also developed an improved formalism for nonlocal interactions that includes deuteron breakup in transfer reactions. This new formalism, the nonlocal adiabatic distorted wave approximation, was used to study the effects of including nonlocality consistently in $(d,p)$ transfer reactions. For the $(p,d)$ transfer reactions, we solved the nonlocal scattering and bound state equations using the Perey-Buck type interaction, and compared to local equivalent calculations. Using the distorted wave Born approximation we construct the T-matrix for $(p,d)$ transfer on $^{17}$O, $^{41}$Ca, $^{49}$Ca, $^{127}$Sn, $^{133}$Sn, and $^{209}$Pb at $20$ and $50$ MeV. Additionally we studied $(p,d)$ reactions on $^{40}$Ca using the the nonlocal dispersive optical model. We have also included nonlocality consistently into the adiabatic distorted wave approximation and have investigated the effects of nonlocality on on $(d,p)$ transfer reactions for deuterons impinged on $^{16}$O, $^{40}$Ca, $^{48}$Ca, $^{126}$Sn, $^{132}$Sn, $^{208}$Pb at $10$, $20$, and $50$ MeV. We found that for bound states the Perry corrected wave functions resulting from the local equation agreed well with that from the nonlocal equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception for a few partial waves. Nonlocality in the proton scattering state reduced the amplitude of the wave function in the nuclear interior. The same was seen for nonlocality in the deuteron scattering state, but the wave function was also shifted outward. In distorted wave Born approximation studies of $(p,d)$ reactions using the Perey-Buck potential, we found that transfer distributions at the first peak differed by $15-35\%$ as compared to the distribution resulting from local potentials. When using the dispersive optical model, this discrepancies grew to $\approx 30-50\%$. When nonlocality was included consistently within the adiabatic distorted wave approximation, the disagreement was found to be $\sim 40\%$. If only local optical potentials are used in the analysis of experimental $(p,d)$ or $(d,p)$ transfer cross sections, the extracted spectroscopic factors may be incorrect by up to $50\%$ in some cases due to the local approximation. This highlights the necessity to pursue reaction formalisms that include nonlocality exactly.
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