  Buildings have been introduced by J. Tits in order to study semi-simple
algebraic groups from a geometrical point of view. One of the most important
results in the theory of buildings is the classification of irreducible
spherical buildings of rank at least 3. About 25 years ago, M. Ronan and J.
Tits defined the class of twin buildings, which generalize spherical buildings
in a natural way. The motivation of their definition is provided by the theory
of Kac-Moody groups.
  A 2-spherical twin building is uniquely determined by its local structure in
almost all cases: The so-called foundation is the union of the rank 2 residues
which contain an (arbitrary) chamber. Therefore, the classification of
2-spherical twin buildings reduces to the classification of all foundations
which can be realized as the local structure of such a twin building. We call
such a foundation "integrable".
  By a result of Tits, an integrable foundation is Moufang, which means that
the rank 2 buildings in the foundation are Moufang polygons, and that the
glueings are compatible with the Moufang structures induced on the rank 1
residues. As a consequence, the classification of Moufang polygons and the
solution of the isomorphism problem for Moufang sets are essential to work out
which Moufang polygons fit together in order to form a foundation.
  The present thesis contributes to establish complete lists of integrable
foundations for certain types of diagrams, namely for simply laced diagrams and
for 443 triangle diagrams. In this process, we closely follow the approach for
the classification of spherical buildings. However, we have to refine the
techniques used there, since in general, foundations don't only depend on the
diagram and the defining field.
  Moreover, one of the main results in the context of Moufang sets is the
solution of the isomorphism problem for Moufang sets of pseudo-quadratic
spaces.
