Notes for Beginner Fourier Analysis?

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

• 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".

Are you acquainted with Brad Osgood's notes?

• The Fourier Transform and its Applications [pdf]

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