This volume explores, explains, and supports the case for an advanced exotic beam facility from a theoretical perspective. The US nuclear physics community and the US Department of Energy are committed to building such a facility. The topics covered constitute a survey of present activities in nuclear theory that will set the challenges for an advanced exotic-beam facility and provide the starting point for interpreting experiments that will be conducted there. The research programs described are all at the forefront of nuclear theory, and they include research on the detailed structures of the lightest nuclei, systematic descriptions of all observed nuclei, nuclear tests of fundamental symmetries of nature, the explosion mechanisms of supernovae, and astrophysical synthesis of the heavy elements, as well as several other topics.