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This book comes as a result of the research work developed in the framework of two large international projects: the European Science Foundation (ESF) supported program NATEMIS (Nonlinear Acoustic Techniques for Micro-Scale Damage Diagnostics) (of which Professor Delsanto was the European coordinator, 2000-2004) and a Los Alamos-based network headed by Dr. P.A. Johnson. The main topic of both programs and of this book is the description of the phenomenology, theory and applications of nonclassical Nonlinearity (NCNL). In fact NCNL techniques have been found in recent years to be extremely powerful (up to more than 1000 times with respect to the corresponding linear techniques) in a wide range of applications, including Elasticity, Material Characterization, Ultrasonics, Geophysics to Maintenance and Restoration of artifacts (paintings, stone buildings, etc.). The book is divided into three parts: Part I - defines and describes the concept of NCNL and its universality and reviews several fields to which it may apply; Part II - describes the phenomenology, theory, modelling and virtual experiments (simulations); Part III - discusses some of the most relevant experimental techniques and applications.