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This book extensively explores the basic principles of quantum-statistical thermodynamics as applied to various states of matter - ranging from rare gases to astrophysical matter with high-energy density. The reader will learn that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of our Universe is in the state of gases and plasmas, and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interiors of stars. Combining material from lectures and advanced seminars given by the authors over many decades, this text is a must-have introduction and reference for both newcomers and seasoned researchers alike.