  The Klein group contains only four elements. Nevertheless this little group
contains a number of remarkable entry points to current highways of modern
representation theory of groups. In this paper, we shall describe all possible
ways in which the Klein group can act on vector spaces over a field of two
elements. These are called representations of the Klein group. This description
involves some powerful visual methods of representation theory which builds on
the work of generations of mathematicians starting roughly with the work of K.
Weiestrass. We also discuss some applications to properties of duality and
Heller shifts of the representations of the Klein group.
