Topological vector spaces book recommendation

I am not sure what your level is (whether you are comfortable with Rudin's functional analysis and Evans). I think Conway's book might be a good reference on topological vector spaces, though a lot of important concepts are not covered. If you find Conway's book to be too easy or too boring for you, then maybe Rudin's book is a better choice. There are plenty of PDE experts in the forum, so I am sure you can get more input from them. If you seek a golden reference from a fields medalist, then you can try Grothendieck 's book, which might be outdated and dense, but addressed topics often not found in modern TVS textbooks.

Update:

I was clearly ignorant, but I found Roberston&Roberston to be really delightful to read. In particular it has a nice chapter on projective tensor products for Frechet spaces, which is often absent from other sources.