In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 × E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the ellipticallyfibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetiˇc, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) U(1) abelian gauge symmetry. They found that in the U(1) × U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by constructing general F-theory compactifications with U(1) × U(1) × U(1) abelian gauge symmetry. I showed that in the case with three U(1) factors, the general elliptic fiber is a complete intersection of two quadrics in P3, and the general elliptic fiber in the fully resolved elliptic fibration is embedded as the generic Calabi-Yau complete intersection into Bl3P3, the blow-up of P3 at three generic points. This eventually leads to our analysis of representations of massless matter at codimension two singularities of these compactifications. Interestingly, we obtained a tri-fundamental representation which is unexpected from perturbative Type II compactifications, further illustrating the power of F-theory. In chapter 1 of this dissertation, I proved finiteness of a region of the string landscape in Type IIB compactifications. String compactifications give rise to a collection of effective low energy theories, known as the string landscape. However, it is not known whether the number of physical theories we can derive from the string landscape is finite. The vastness of the string landscape also poses a serious challenge to attempts of studying it. A breakthrough was made by Douglas and Taylor in 2007 when they studied the landscape of intersecting brane models in Type IIA compactifications on a particular Z2× Z2 orientifold. They found that two consistency conditions, namely the D6-brane tadpole cancellation condition, and the conditions on D6-branes that were required for N = 1 supersymmetry in four dimensions, only permitted a finite number of D6-brane configurations. These finite number of allowed D6-brane configurations thus result in only a finite number of gauge sectors in a 4D supergravity theory, allowing them to be studied explicitly. Douglas and Taylor also believed that the phenomenon of using tadpole cancellation and supersymmetry consistency conditions to restrict the possible number of allowed configurations to a finite one is not a mere coincidence unique to their construction; they conjectured that this phenomenon also holds for theories with magnetised D9- or D5-branes compactified on elliptically fibered Calabi-Yau threefolds. Indeed, this was what my collaborators and I also felt. To this end, I showed, using a mathematical proof, that their conjecture is indeed true for elliptically fibered Calabi-Yau threefolds p X B whose base B satisfy a few easily-checked conditions (summarized in chapter 1 of this dissertation). In particular, these conditions are satisfied by, although not limited to, the almost Fano twofold bases B given by the toric varieties associated to all 16 reflexive two-dimensional polytopes and the del Pezzo surfaces dPn for n = 0;1;