Optimal Transportation, Geometry and Functional Inequalities

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In 2008, a school on the theory of Optimal Transportation and its applications took place in Pisa, with lectures by F. Barthe, W. Gangbo, F. Maggi, R. McCann. In this book, the notes of the first three lecturers are collected. They provide a deep insight on concentration inequalities, evolution PDEs of Hamiltonian type, geometric and functional inequalities.