  Motivated by potential phenomenological applications, we develop the
necessary tools for building GUT models in F-theory. This approach is quite
flexible because the local geometrical properties of singularities in F-theory
compactifications encode the physical content of the theory. In particular, we
show how geometry determines the gauge group, matter content and Yukawa
couplings of a given model. It turns out that these features are beautifully
captured by a four-dimensional topologically twisted N=4 theory which has been
coupled to a surface defect theory on which chiral matter can propagate. From
the vantagepoint of the four-dimensional topological theory, these defects are
surface operators. Specific intersection points of these defects lead to Yukawa
couplings. We also find that the unfolding of the singularity in the F-theory
geometry precisely matches to properties of the topological theory with a
defect.
