  This thesis is concerned with heterotic E8 x E8 string models that can
produce quasirealistic N = 1 supersymmetric extensions of the Standard Model in
the low-energy limit. We start rather generally by deriving the
four-dimensional spectrum and Lagrangian terms from the ten-dimensional theory,
through a process of compactification over six-dimensional Calabi-Yau
manifolds, upon which holomorphic poly-stable vector bundles are defined. We
then specialise to a class of heterotic string models for which the vector
bundle is split into a sum of line bundles and the Calabi-Yau manifold is
defined as a complete intersection in projective ambient spaces. We develop a
method for calculating holomorphic Yukawa couplings for such models, by
relating bundle-valued forms on the Calabi-Yau manifold to their ambient space
counterparts, so that the relevant integrals can be evaluated over projective
spaces. The method is applicable for any of the 7890 CICY manifolds known in
the literature, and we show that it can be related to earlier algebraic
techniques to compute holomorphic Yukawa couplings. We provide explicit
calculations of the holomorphic Yukawa couplings for models compactified on the
tetra-quadric and on a co-dimension two CICY. A vanishing theorem is
formulated, showing that in some cases, topology rather than symmetry is
responsible for the absence of certain trilinear couplings. In addition, some
Yukawa matrices are found to be dependent on the complex structure moduli and
their rank is reduced in certain regions of the moduli space. In the final
part, we focus on a method to evaluate the matter field Kahler potential
without knowing the Ricci-flat Calabi-Yau metric. This is possible for large
internal gauge fluxes, for which the normalisation integral localises around a
point on the compactification manifold.
