Who is A in pretty little liars?

at the beggining, Mona is A. then hanna kills her by pushing her off a ledge, then Ali takes over. the "Ali" they were friends with was actually Courtney, who had a multiple personality disorder. In the show, i don't know what ian has to do with it, but in the book he doesn't really. In room 214 is just a bag of ice that has a note from A that says "you're getting colder" because they can't figure anything out. hope this helps