  In this Master thesis we consider 't Hooft's polygon model for 2+1D gravity.
After a detailed review of the polygon model in the classical context, we
discuss problems associated with its quantization and calculate the explicitly
the full Poisson structure of the constraints.
  The calculation of the Poisson structure in chapter 6 introduces corrections
and generalizations to earlier published results. We show that the full Poisson
structure closes on shell, but not off shell. An attempt is made to interpret
the gauge orbits generated by the constraints.
