The primary motivation for studying nucleus-nucleus collisions at relativistic and ultrarelativistic energies is to investigate matter at high energy densities ([var-epsilon] [much-gt] 1 GeV/fm[sup 3]). Early speculations of possible exotic states of matter focused on the astrophysical implications of abnormal states of dense nuclear matter. Field theoretical calculations predicted abnormal nuclear states and excitation of the vacuum. This generated an initial interest among particle and nuclear physicists to transform the state of the vacuum by using relativistic nucleus-nucleus collisions. Extremely high temperatures, above the Hagedorn limiting temperature, were expected and a phase transition to a system of deconfined quarks and gluons, the Quark-Gluon Plasma (QGP), was predicted. Such a phase of matter would have implications for both early cosmology and stellar evolution. The understanding of the behavior of high temperature nuclear matter is still in its early stages. However, the dynamics of the initial stages of these collisions, which involve hard parton-parton interactions, can be calculated using perturbative QCD. Various theoretical approaches have resulted in predictions that a high temperature (T [approximately] 500 MeV) gluon gas will be formed in the first instants (within 0.3 fm/c) of the collision. Furthermore, QCD lattice calculations exhibit a phase transition between a QGP and hadronic matter at a temperature near 250 MeV. Such phases of matter may have existed shortly after the Big Bang and may exist in the cores of dense stars. An important question is whether such states of matter can be created and studied in the laboratory. The Relativistic Heavy Ion Collider (RHIC) and a full complement of detector systems are being constructed at Brookhaven National Laboratory to investigate these new and fundamental properties of matter.