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This book presents a study of the fundamental properties of optical and acoustic materials, which have been of recent interest in nanoscience and device technology. With the addition of a new chapter, this Second Edition is an essential resource on the topic, appropriate for advanced undergraduates, beginning graduate students, and researchers. The author begins by reviewing the basic theories of electrodynamics and acoustics and applying them to basic examples. The formulations are extended and developed for the determinations of the modes in photonic and phononic crystals. The book then introduces, discusses, and provides examples of the applications of electromagnetic and acoustic waveguides as well as acoustic and electromagnetic metamaterials. The author also covers the physics of surface electromagnetic and acoustic waves. This Second Edition includes a new chapter introducing topological concepts and the theory and applications of electromagnetic and acoustic metasurfaces.