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Nonlinear acoustics is a relatively new science and is slightly younger than linear acoustics. The main theoretical concept, that is the equations and results of nonlinear acoustics of homogeneous media have already been preconceived, studied in detail, and published in many original papers. However, the research into nonlinear acoustics of microinhomogeneous solids is far from complete, and at present, much work, both experimental and theoretical, is being done.This book is the author's attempt to present a perspective on the wide and incomplete branch of nonlinear acoustics. The introductory chapter presents a review of the main achievements of the classic nonlinear acoustics of the homogeneous media. This enables readers to gain insight into nonlinear wave processess in homogeneous and microinhomogeneous media and compare it within the framework of the book. The subsequent eight chapters are based on the published work of the authors and dedicated to the theoretical and experimental research of the nonlinear processes, caused by longitudinal elastic waves propagation and interaction in the microinhomogeneous media with a strong acoustical nonlinearity of different types (elastic, hysteretic and non-elastic). For convenience of presentation the book presents the theory initially and the experimental results subsequently. The book is intended for students, specialists and for all people, who is interested in nonlinear acoustics.