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Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modeling of these waves has undergone considerable growth in recent years, and this timely book, written by a leading international researcher, presents the research in a careful and complete way.This self-contained book is devoted to the study of the acoustic wave equations and the Maxwell system, the two most common waves equations that are encountered in physics or in engineering. It presents a detailed analysis of their mathematical and physical properties. In particular, the author focuses on the study of the harmonic exterior problems, building a mathematical framework which provides the existence and uniqueness of the solutions. §This book will serve as a useful introduction to wave problems for graduate students in mathematics, physics, and engineering.