I'd like to point out a recent (Birkhäuser Cornerstones) textbook on Distribution Theory by Duistermaat and Kolk.
The present text has evolved from a set of notes for courses taught at Utrecht University over the last twenty years, mainly to bachelor-degree students in their third year of theoretical physics and/or mathematics.
(I have followed this course, which was quite fun.)
For a more advanced exposition, Knapp's Advanced Real Analysis is great.
Very complete and advanced (and dry) is Hörmander's The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, which has already been mentioned.