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The theoretical study of the nuclear equation of state (EOS) is a field of research which touches on most of the fundamental problems in nuclear physics. In this book, an overview of the present status of the microscopic theory of the nuclear Equation of State is given. Its aim is essentially twofold. First, to provide a volume that could be a real textbook for advanced students entering the field by covering the different subjects as exhaustively and didactically as possible. Second, to be a reference book for all researchers active in the theory of nuclear matter by presenting an updated report on the latest developments. Special emphasis will be given to the present numerous open problems and the prospects for their possible solutions. The general framework of the different approaches to be presented in the book is the meson theory of nuclear forces, where no free parameter is introduced, and the many-body treatment of nucleon-nucleon correlations. The ultimate hope of this world-wide effort is the understanding of the structure of nuclear matter, both in the ground state and at finite temperature. The main audience addressed is the community of theoretical nuclear physicists, but nuclear experimentalists and astrophysicists will also find in the book an extensive amount of material of direct interest for their everyday work, particularly for those studying heavy-ion collisions, where the nuclear EOS is of special relevance. Finally, theoretical physicists working on elementary particle theory could find in the book some stimulating ideas and problems directly related to their own field.