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In this volume, five papers are collected that give a good sample of the problems and the results characterizing some recent trends and advances in this theory. Some of them are devoted to the improvement of a general abstract knowledge of the behaviour of elastic bodies, while the others mainly deal with more applicative topics. The first paper entitled "Collected Results on Finite Amplitude Plane Waves in Deformed Mooney-Rivlin Materials" by Ph. Boulanger and M. Hayes gives a complete and systematic exposition of a body of selected results concerning the propagation of finite-amplitude...