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This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way.--Alan Weinstein, University of California at BerkeleyThis well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study.--Eckhard Meinrenken, University of Toronto.

Symplectic geometry --- Poisson brackets --- Poisson manifolds --- Poisson algebras --- Groupoids

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Transport theory --- Microstructure --- Thermodynamics --- Hamiltonian systems. --- Viscoelasticity. --- Poisson brackets. --- Mathematical models. --- -Thermodynamics --- -Hamiltonian systems --- Viscoelasticity --- Poisson brackets --- -Brackets, Poisson --- Poisson's brackets --- Differential equations, Nonlinear --- Continuum mechanics --- Elasticity --- Viscosity --- Relaxation phenomena --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Materials --- Matter --- Morphology --- Micromechanics --- Stereology --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Mathematical models --- Constitution --- Hamiltonian systems --- Microstructures --- Systèmes hamiltoniens --- Transport, Théorie du --- Viscoélasticité --- Modèles mathématiques --- Brackets, Poisson --- Transport theory - Mathematical models. --- Microstructure - Mathematical models. --- Thermodynamics - Mathematical models.