Notes for Beginner Fourier Analysis? Are there any good lecture notes or books on basic fourier analysis that authors publish freely online?
It is very difficult to find rigorous mathematical theory of fourier analysis because google is saturated with practical things since it has so much application in other fields.
Thank you very much.
I only want free as in freedom materials please
 A: 


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*See MIT OCW for lecture notes, and more, for a class on Fourier Analysis, taught by Prof. Richard Melrose of MIT.





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*See also: Lecture notes from Christoph Thiele's webpage (UCLA): scroll down to $(8), (9)$ where you'll find links to notes for two classes he taught: Fourier Analysis $1$ and Fourier analyis $2$. The notes are posted by the author, and available to download in ps and/or pdf formats.



You might be interested, too, in the tutorial "A Pictorial Introduction to Fourier Analysis", and the associated web-page with links to other resources for understanding fourier analysis in various contexts.

One text that you might want to think about borrowing from your library, or obtaining through inter-library loan, is Stein and Shakarchi's Fourier Analysis: An Introduction, one book of three in the series: "Princeton Lectures in Analysis".
A: Are you acquainted with Brad Osgood's notes?


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*The Fourier Transform and its Applications [pdf]


If you're looking for "purer" Harmonic Analysis material, try Yitzhak Katznelson's book.
A: See Introduction to Fourier Analysis by Arthur Schoenstadt or, for something more advanced, these harmonic analysis notes by Wilhelm Schlag which are being reworked into a book.
A: Here is a good book by "E. C Titchmarsh" but I do not know if you can get a free copy "Introduction to the theory of Fourier integrals"
A: Tom Wolff published a collection of notes titled "Lectures on Harmonic Analysis" which he made freely available.  Since his passing, the notes have been kept on Izabella Laba's website.  The notes are superbly written and well motivated, and the website to which I linked also has a list of errata.
