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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

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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".

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Thanks a lot, this looks really nice. – user51427 Dec 10 '12 at 16:50
You're welcome, sunflower! – amWhy Dec 10 '12 at 18:15

Are you acquainted with Brad Osgood's notes?

If you're looking for "purer" Harmonic Analysis material, try Yitzhak Katznelson's book.

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Osgood notes and the book about applications looks great thanks a lot! – user51427 Dec 10 '12 at 17:01
Stanford has his lectures online as well. He's really a pretty funny guy! – user4536 Feb 8 '13 at 22:02

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.

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Thanks a lot! w – user51427 Dec 10 '12 at 17:01

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"

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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.

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