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The Facility for Antiproton and Ion Research (FAIR) will employ the World's highest intensity relativistic beams of heavy nuclei to uniquely create and investigate macroscopic (millimeter-sized) quantities of highly energetic and dense states of matter. Four principal themes of research have been identified: properties of materials driven to extreme conditions of pressure and temperature, shocked matter and material equation of state, basic properties of strongly coupled plasma and warm dense matter, and nuclear photonics with a focus on the excitation of nuclear processes in plasmas, laser-driven particle acceleration, and neutron production. The research program, principally driven by an international collaboration of scientists, called the HED@FAIR collaboration, will evolve over the next decade as the FAIR project completes and experimental capabilities develop. The first programmatic research element, called "FAIR Phase 0, officially began in 2018 to test components, detectors, and experimental techniques. Phase-0 research employs the existing and enhanced infrastructure of the GSI Helmholtzzentrum für Schwerionenforschung (GSI) heavy-ion synchrotron coupled with the PHELIX high-energy, high-intensity laser. The "FAIR Day one" experimental program, presently scheduled to begin in 2025, commences the use of FAIR's heavy-ion synchrotron, coupled to new experimental and diagnostic infrastructure, to realize the envisaged high-energy-density-science research program.