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Understanding the nature of strongly interacting nuclear matter requires a fundamental description of nucleons starting with the individual quarks and gluons and ending with a description of nuclei and their structure.  Surprisingly, even the structures of the proton and neutron remain undetermined, and the challenge of describing nucleons within the framework of Quantum Chromodynamics complements that of understanding the nucleus from the interaction of the constituent nucleons.  The most extreme test of nuclear matter occurs when nuclei collide at energies at which the energy density reaches five times normal nuclear matter density, providing a laboratory test of the nature of matter a short instant after the Big Bang.  Extremes of matter also occur in violent stellar processes such as supernovae and X-ray bursters in binary stars, thought to give rise to the synthesis of many of the heavier elements that exist naturally on Earth.