Understanding the properties of the dense ionized matter found in the interiors of low-mass stars and giant planets is one of the major challenges facing physicists. In this volume, world experts in plasma and dense matter physics and in stellar astrophysics review everything from the cooling theory of white dwarfs and their accretion-induced collapse to the internal structure of low-mass stars and giant planets. They also cover a wide range of topics related to the equation of state in dense matter, from the fundamental basis of the N-body problem, to the astrophysical applications. Together these articles provide an essential review of the most recent achievements in the field and give direction for future research for graduate students and researchers.