Harry's ready for his 3rd year at Hogwarts School of Witchcraft and Wizardry, but it isn't going to be the calm year he hoped for. The infamous murder, Sirius Black evidently wants him dead and the school is being gaurded by Dementors who seem to effect Harry worse than anyone else. At least he's got his best friends Ron and Hermione to help him through lessons, and a new favorite teacher in Remus Lupin, who might hold more information than Harry could imagine.
Prisoner of Azkaban is a changing point in the series. We are given a handful of new, important characters in Sirius Black, Remus Lupin and Peter Pettigrew, as well as the biggest appearance of Minster for Magic Cornelius Fudge. With the help of these amazing new characters we get light handed exposition that rockets the entire series forward in a way that makes starting Goblet of Fire difficult to put off.
It is in Prisoner of Azkaban that Rowling really seems to have found her characters. Harry grows into his own as he deals with images of his parents death and new knowledge of what caused it. While Harry has always outwardly been a hero, it is here that his internal compass catches up to him. Ron and Hermione also have great growth. Hermione continues to test her theory that there are things more important than rules, and Ron shows that he is deeply capable of love, even if it is for a disguised rat.
Prisoner of Azkaban is pretty much a universal favorite. Now that we have spent two books with all of the major players we're given interesting plot devices and back story. My only issue with it is that, like the previous two, all of the action is crammed into the last 70 pages and sometimes the set up doesn't get the intensity of payoff one would expect.
I'm off to finish Goblet of Fire!