Research will be concerned with theoretical elementary particle physics. From particle accelerators a great deal has been learned about the fundamental behavior of the quarks that compose protons even though the quarks have never escaped from protons. However, calculations show that at extremely high temperatures (1010 times room temperature) and extremely high densities (1015 times normal), protons will melt into a fluid composed of unconfined quarks. These conditions occurred in the very early universe and will be recreated in accelerators now being built to collide heavy nucleii. This project is intended to help develop reliable methods for calculating the behavior of quarks and gluons under these extreme conditions. This is important to our efforts to achieve an understanding of the early universe and of the behavior of nuclear matter at high temperatures and densities.