  At high temperatures or densities matter formed by strongly interacting
elementary particles (hadronic matter) is expected to undergo a transition to a
new form of matter - the quark gluon plasma - in which elementary particles
(quarks and gluons) are no longer confined inside hadrons but are free to
propagate in a thermal medium much larger in extent than the typical size of a
hadron. The transition to this new form of matter as well as properties of the
plasma phase are studied in large scale numerical calculations based on the
theory of strong interactions - Quantum Chromo Dynamics (QCD). Experimentally
properties of hot and dense elementary particle matter are studied in
relativistic heavy ion collisions such as those currently performed at the
relativistic heavy ion collider (RHIC) at BNL. We review here recent results
from studies of thermodynamic properties of strongly interacting elementary
particle matter performed on Teraflops-Computer. We present results on the QCD
equation of state and discuss the status of studies of the phase diagram at
non-vanishing baryon number density.
