Continuing through the series as I am never one to stop part way through, Harry Potter and the Prisoner of Azkaban is possibly my favorite of the series. Its a healthy crossing point between the childlike fantasy of the early books, and the more serious tone the later ones start to form.
The Prisoner of Azkaban adds some wonderful worldbuilding to the universe, revealing of course, the presence of both a Wizard’s prison, and the fact that Potter has a godfather. You really get a feeling for just how off balance the wizarding world is, even years after Voldemort’s disappearance, and how even in a magical realm, the legal system can be corrupt, and unjust.
In my opinion, if the first two books don’t sell you on the series, this one should, as it feels like here is where it begins to really step into its own.