I was wondering if anyone had any good suggestions on distribution theory books. I am looking for one that would be a good solid introduction for a graduate student in mathematics (or even an advanced undergraduate book). Example topics would include smooth test functions with compact support, distributions, examples of distributions, equivalent definitions of distributions, Schwartz structure theorem, Frechet space, semi-norms, support of a distribution, patching distributions, distributions with compact support, Schwartz functions, Fourier transforms, tempered distributions, etc. I have found a few books, but decided not to list them to see what others like enough to suggest. I would use such a book to complement a course right now, and then hopefully later, to write some introductory notes of my own.