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This graduate and advanced undergraduate textbook systematically addresses all core topics in physical and engineering acoustics. Written by a well-known textbook author with 39 years of experience performing research, teaching, and mentoring in the field, it is specially designed to provide maximum support for learning. Presentation begins from a foundation that does not assume prior study of acoustics and advanced mathematics. Derivations are rigorous, thoroughly explained, and often innovative. Important concepts are discussed for their physical implications and their implementation. Many of the examples are mini case studies that address systems students will find to be interesting and motivating for continued study. Step-by-step explanations accompany example solutions. They address both the significance of the example and the strategy for approaching it. Wherever techniques arise that might be unfamiliar to the reader, they are explained in full. Volume I contains 186 homework exercises, accompanied by a detailed solutions manual for instructors. This text, along with its companion, Volume II: Applications, provides a knowledge base that will enable the reader to begin undertaking research and to work in core areas of acoustics.