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This book is dedicated to the theory of supernovae, focussing on new computational methods and simulations. It contains three parts: basic principles, numerical methods, and applications. The first part contains the non-formal introduction into the topics of supernovae, Boltzmann kinetic equations - with details of two particles reaction rate calculations - and the transformation of Boltzmann kinetic equations into hydrodynamic elements of statistical physics. It contains the equation of state for matter of high energy density, with details of calculations for thermodynamic parameters, weak interactions reaction rate details, and thermonuclear burning. The second part introduces elements of computational physics. The book collects not only generally accepted simulations methods, it also includes original approaches of the authors from two Russian groups in Supernovae, from the Keldysh Institute of Applied Mathematics and Institute for Theoretical and Experimental Physics. The book closes with a presentation of original works about the regime of burning in degenerate carbon-oxygen cores, a neutrino transport in supernovae type II, simulation of GR coalescence of neutron stars, aspherical nucleosynthesis in a core-collapse supernova, and thermalization in pair of plasma wind from a compact strange star. It contains the necessary information for a person to start independent research in this fast-developing field. It is therefore an important read for new researchers in this subject.

Supernovae. --- Supernovae --- Mathematical models. --- Modèles mathématiques.