"Classical Fourier Analysis" is a second edition textbook by Loukas Grafakos, designed for graduate students studying Fourier analysis. The book is structured as a one-semester course, with prerequisites in measure theory, Lebesgue integration, and complex variables. It covers fundamental topics in Fourier analysis, including $ L^p $ spaces, interpolation, maximal functions, Fourier transforms, distributions, convolution operators, and singular integrals. The text also includes discussions on Fourier series, convergence, and the theory of singular integrals, as well as applications to harmonic analysis and partial differential equations. The book provides detailed proofs and includes exercises at the end of each section to reinforce understanding. Historical notes are included to provide context and suggest further research directions. An appendix contains auxiliary material, and a web site is provided for additional resources. The second edition includes corrections and improvements based on feedback from readers and contributors. The book is divided into chapters covering various aspects of Fourier analysis, including topics such as Lorentz spaces, oscillatory integrals, Fourier analysis on the torus, singular integrals, Littlewood-Paley theory, and wavelets. It also includes appendices on special functions, Bessel functions, Rademacher functions, spherical coordinates, trigonometric identities, and other mathematical tools. The text is well-organized and suitable for both self-study and as a course textbook."Classical Fourier Analysis" is a second edition textbook by Loukas Grafakos, designed for graduate students studying Fourier analysis. The book is structured as a one-semester course, with prerequisites in measure theory, Lebesgue integration, and complex variables. It covers fundamental topics in Fourier analysis, including $ L^p $ spaces, interpolation, maximal functions, Fourier transforms, distributions, convolution operators, and singular integrals. The text also includes discussions on Fourier series, convergence, and the theory of singular integrals, as well as applications to harmonic analysis and partial differential equations. The book provides detailed proofs and includes exercises at the end of each section to reinforce understanding. Historical notes are included to provide context and suggest further research directions. An appendix contains auxiliary material, and a web site is provided for additional resources. The second edition includes corrections and improvements based on feedback from readers and contributors. The book is divided into chapters covering various aspects of Fourier analysis, including topics such as Lorentz spaces, oscillatory integrals, Fourier analysis on the torus, singular integrals, Littlewood-Paley theory, and wavelets. It also includes appendices on special functions, Bessel functions, Rademacher functions, spherical coordinates, trigonometric identities, and other mathematical tools. The text is well-organized and suitable for both self-study and as a course textbook.