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This is an excellent book for advanced students and researchers who wish to know more about a rapidly expanding subfield of differential equations that has recently seen important new developments. The authors do an excellent job in providing a technically polished, yet readable account of the state-of-the-art for multi-dimensional systems of hyperbolic PDE. Working in this field, I am grateful that Benzoni-Gavage and Serre have performed this task. I believe this will become a standard reference in the coming years.