  The moduli space of flat SL(2,R)-connections modulo gauge transformations on
the torus may be described by ordered pairs of commuting SL(2,R) matrices
modulo simultaneous conjugation by SL(2,R) matrices. Their spectral properties
allow a classification of the equivalence classes, and a unique canonical form
is given for each of these. In this way the moduli space becomes explicitly
parametrized, and has a simple structure, resembling that of a cell complex,
allowing it to be depicted. Finally, a Hausdorff topology based on this
classification and parametrization is proposed.
