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b'As of now, string theory is the best candidate for a theory of quantum gravity. Since it is anomaly\\u2013free only in ten space-time dimensions, the six surplus spatial dimensions must be compactified. \\nThis thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. An orbifold is the quotient of a smooth manifold by a discrete \\ngroup. In the present thesis, we restrict ourselves to orbifolds of the form T^6 /Z_N or T^6 /Z_N \\xd7 Z_M . These so\\u2013called toroidal orbifolds are particularly popular as compactification manifolds in string theory. They present a good compromise between a trivial compactification manifold, such as the T^6 and one which is so complicated that explicit calculations are nearly impossible, which unfortunately is the case for many if not most Calabi\\u2013Yau manifolds. At the fixed points of the discrete group which is divided out, the orbifold develops quotient singularities. By resolving these singularities via blow\\u2013ups, one arrives at a smooth Calabi\\u2013Yau manifold. The systematic method to do so is explained in detail. Also the transition to the Orientifold quotient is explained. \\nIn string theory, toroidal orbifolds are popular because they combine the advantages of calculability and of incorporating many features of the standard model, such as non-Abelian gauge groups, chiral fermions and family repetition. \\nIn the second part of this thesis, applications in string phenomenology are discussed. The applications belong to the framework of compactifications with fluxes in type \\nIIB string theory. Flux compactifications on the one hand provide a mechanism for supersymmetry breaking. One the other hand, they generically stabilize at least part \\nof the geometric moduli. The geometric moduli, i.e. the deformation parameters of the compactification manifold correspond to massless scalar fields in the low energy \\neffective theory. Since such massless fields are in conflict with experiment, mechanisms which generate a potential for them and like this fix the moduli to specific values \\nmust be investigated. After some preliminaries, two main examples are discussed. The first belongs to the category of model building, where concrete models with realistic \\nproperties are investigated. A brane model compactified on T^6 /Z_2 \\xd7 Z_2 is discussed. \\nThe flux-induced soft supersymmetry breakingparameters are worked out explicitly. \\nThe second example belongs to the sub ject of moduli stabilization along the lines of the proposal of Kachru, Kallosh, Linde and Trivedi (KKLT). Here, in addition to the \\nbackground fluxes, non-perturbative effects serve to stabilize all moduli. In a second step, a meta-stable vacuum with a small positive cosmological constant is achieved. \\nOrientifold models which result from resolutions of toroidal orbifolds are discussed as possible candidate models for an explicit realization of the KKLT proposal. \\nThe appendix collects the technical details for all commonly used toroidal orbifolds \\nand constitutes a reference book for these models.'