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This book originated from lecture notes on graduate-level harmonic analysis that I have taught over the years at the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, as well as at Capital Normal University.
It is intended for graduate students and advanced undergraduates with a solid background in real analysis, functional analysis, and complex analysis. The book is designed to be accessible to readers at different levels, providing both depth and clarity. The background material and key notations are introduced in Appendix A, making the text approachable even for those less familiar with certain topics. Each chapter is structured with carefully chosen exercises, which are integral for reinforcing understanding and facilitating self-study. This makes the book suitable for independent learners who wish to progress at their own pace. Whether used as a textbook in formal courses or as a resource for self-guided study, the book aims to meet the needs of a wide range of learners.
The material presented draws on a variety of sources, including foundational texts as well as online lecture notes, with appropriate modifications throughout. While we do not provide extensive heuristics or motivational background, our primary goal is to present each proof in a clear, step-by-step manner to facilitate comprehension.