  This paper is devoted to the study of affine quaternionic manifolds and to a
possible classification of all compact affine quaternionic curves and surfaces.
It is established that on an affine quaternionic manifold there is one and only
one affine quaternionic structure. A direct result, based on the celebrated
Kodaira Theorem that studies compact complex manifolds in complex dimension 2,
states that the only compact affine quaternionic curves are the quaternionic
tori and the primary Hopf surface S^3 x S^1. As for compact affine quaternionic
surfaces, we restrict to the complete ones: the study of their fundamental
groups, together with the inspection of all nilpotent hypercomplex simply
connected 8-dimensional Lie Groups, identifies a path towards their
classification.
