"Classical Fourier Analysis" is a comprehensive textbook that deals with the theoretical foundations of Fourier analysis. It is primarily aimed at graduate-level mathematics students and is designed for a three-semester course series. The only prerequisite for understanding the text is the successful completion of a course in measure theory, Lebesgue integration, and complex variables. The book thoroughly covers selected topics in Fourier analysis and encourages further exploration. While the focus is on methods with real variables in Euclidean spaces, there is also a chapter on the fundamentals of analysis on the torus to illustrate the historical development of Fourier analysis. The new edition includes 120 pages of new material, including an additional chapter on time-frequency analysis and other modern topics, and will be published in two volumes, with the first volume covering classical topics and the second volume covering modern topics.