to tell how complex the study of modular representations can be for an arbitrary group.

Now we turn to the second question. Although the classification of the finite dimensional representations of $V_{4}$ is well-known and many proofs can be found in the literature, we could not find a proof to our heart’s content. This is what motivated us to write up one – one that is transparent and which takes a minimal background. Furthermore, our approach is diagrammatic, so the reader can see what is happening through pictures. These methods, besides making the statements of theorems and proofs elegant and conceptual, give a better insight into the subject. We mostly follow Benson’s approach [@ben-1] but we approach some parts of his proof from a different point of view and simplify them and in particular we make our proof accessible for a general reader. One ingredient that is new in our approach is Auslander-Reiten sequences which will be introduced later in the paper.

The subject of classifying the indecomposable representations of the Klein group has a long and rich history that can be traced all the way back to V. A. Bašev [@basev], a student of I.R. Šafarevič, who observed that 