All papers were peer-reviewed. The aim of the workshop was to bring together physicists and astronomers with an interest in this interdisciplinary field. Breakthroughsannounced during the workshop include: a report that a near-ten-year controversy about high-pressure experiments with hydrogen and deuterium has ended; a demonstration that dynamical effects in screening enhancements of nuclear reactions must be taken seriously; a critical assessment of systematic errors in observational helioseismological data; and a collective relaization that right now there is a remarkable number of independent advanced formalisms for astrophysically useful equations of state.