  The complete classification of representations of the Trefoil knot group G in
S^{3} and SL(2,R), their affine deformations, and some geometric
interpretations of the results, are given. Among other results, we also obtain
the classification up to conjugacy of the non cyclic groups of affine Euclidean
isometries generated by two isometries $\mu$ and $\nu$ such that
$\mu^{2}=\nu^{3}=1$, in particular those which are crystallographic. We also
prove that there are no affine crystallographic groups in the three dimensional
Minkowski space which are quotients of G.
