  It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and
$R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of
  2D NonEinsteinian Gravity. Different approaches to the formulation of a
quantum theory for the above systems are then presented: The Dirac constraints
can be solved exactly in the momentum representation, the path integral can be
integrated out, and the constraint algebra can be {\em explicitely} canonically
abelianized, thus allowing also for a (superficial) reduced phase space
quantization. Non--trivial dynamics are obtained by means of time dependent
gauges. All of these approaches lead to the {\em same} finite dimensional
quantum mechanical system.
