Parsian, Mohammadhadi2020-05-072020-05-072020-05-06vt_gsexam:25359http://hdl.handle.net/10919/97995In the first part of this thesis, we investigate a way to find the complex structure moduli, for a given background of type IIB string theory in the presence of flux in special cases. We introduce a way to compute the complex structure and axion dilaton moduli explicitly. In the second part, we discuss $(0,2)$ supersymmetric versions of some recent exotic $mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models, describing intersections of Grassmannians. In the next part, we consider mirror symmetry for certain gauge theories with gauge groups $F_4$, $E_6$, and $E_7$. In the last part of this thesis, we study whether certain branched-double-cover constructions in Landau-Ginzburg models can be extended to higher covers.ETDIn CopyrightType IIB string theoryFlux compactificationsModuliCohomologyNon-abelian supersymetric gauge theoryDissertation