There are many good books on functional analysis, e.g.:

Walter Rudin, Functional Analysis, McGraw Hill, 1973 (Very good and widely used textbook, reprinted many times. Perhaps the best reading if you are interested in mathematics and want to learn the functional analysis. Has also a chapter on Fourier transform.)

Sterling Berberian, Lectures in Functional Analysis and Operator Theory, Graduate texts in mathematics, Springer, 1973, (Another very good general textbook, I personally prefer Rudin, but for some aspects this one is better.)

Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional Analysis, Academic Press, 1980 (First part of a multi-volume textbook on mathematical physics. It gives a firm functional analysis background for use in the mathematical physics)

If you are interested in further reading, please ask and we will find something.