I review Klaus Kinder-Geiger’s contributions to the physics of relativistic heavy ion collisions, in particular, the Parton Cascade Model. Klaus developed this model in order to provide a QCD–based description of nucleus-nucleus reactions at high energies such as they will soon become available at the Brookhaven Relativistic Heavy Ion Collider. The PCM describes the collision dynamics within the early and dense phase of the reaction in terms of the relativistic, probabilistic transport of perturbative excitations (partons) of the QCD vacuum. I will present an overview of the current state of the numerical implementations of this model, as well as its predictions for nuclear collisions at RHIC and LHC. ©1999 American Institute of Physics.