  The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as
the holonomy of a torsion-free affine connection on an n-manifold are
classified, thus completing the work on this subject begun by M. Berger in the
1950s. The methods employed include representation theory, the theory of
hermitian symmetric spaces, twistor theory, and Poisson geometry. The latter
theory is especially important for the construction and classification of those
torsion-free connections whose holonomy falls into one of the so-called
`exotic' cases, i.e., those that were not included in Berger's original lists.
Some remarks involving an interpretation of some of the examples in terms of
supersymmetric constructions are also included.
