After reading several strong players say that it's best to study tactics by theme / category (pins, fork, skewers etc.) to really develop that pattern recognition, I really want to train that way. Unfortunately chess.com's tactics trainer is just a random assembly of puzzles. What I would like is a book (or website / program) that orders tactics by theme.

Is there any such resource available for one of my rating? (1300)

i think its the best method. CT ART of course

die

joking

I use CT-ART 3.0 and sort by theme.

Aha. I already use "Chess tactics for beginners 2.0" which looks exactly like CT-Art. Do they share the same interface or something?

Anyway, would you recommend CT-Art over CTFB 2.0?

I have never used CTFB so i cant give an opinion.  But since CT-ART is consistently voted the best tactics training software, and the problems come from real games, i would highly recommend it.  

Thanks, will prolly get CT-Art 5 then.

I would also like just one book that has tactics arranged by theme, do you know a good one for that?

That would depend on your skill level.  There are many really good tactics books, but they each cater to a diffeent skill set.  The following 2 are a good start:

Tim Brennan: Tactics Time! 1001 Chess Tactics from the Games of Everyday Chess Players, is an excellent beginners tactics book.  

Susan Polgar: Chess Tactics for Champions: A step-by-step guide to using tactics and combinations the Polgar way, is a step up from the first book.

With the tactics trainer here, you can select puzzles by themes in unrated mode.

How so? I can't find it.

You have to be over on V3.  ("Try the new Chess.com" at the bottom of every page)

And then select training mode Custom (unrated). You get a list from where you can select themes.