The main resolution:
* Sirius Black is proven innocent: Through a series of events, including Harry's time turner use, Sirius's escape from Azkaban, and his subsequent confrontation with Peter Pettigrew, the truth about Sirius's innocence is revealed.
* Peter Pettigrew is captured: Pettigrew, the real traitor and murderer, is exposed and captured by the Order of the Phoenix. This ends the immediate threat to Harry.
* Sirius Black's true intentions: Sirius Black, Harry's godfather, is cleared of any wrongdoing and revealed to be a good and loyal friend. He expresses his desire to be Harry's guardian, a role that ultimately doesn't happen due to the time turner being destroyed.
* Hermione Granger saves the day: Through her clever use of the time turner, Hermione not only saves herself and Harry from danger, but also ensures the events leading to the revelation of the truth happen in the correct order.
Other resolutions:
* The Dementors are expelled from Hogwarts: As a result of Sirius Black's escape and the revelation that Dementors were not reliable in guarding prisoners, they are expelled from Hogwarts.
* Harry and Ron's friendship is strengthened: Despite some disagreements, Harry and Ron's friendship is reaffirmed throughout the ordeal.
* The mystery of the Marauder's Map is solved: The identity of the Marauders, the creators of the map, and the meaning behind their "secret" is unveiled, adding to the overall resolution.
The final state:
* Harry, Ron, and Hermione are safe and sound at Hogwarts, having overcome a dangerous ordeal.
* The school is back to normal, with a new Defense Against the Dark Arts teacher.
* The threat posed by Sirius Black is eliminated, and the real villain, Peter Pettigrew, is apprehended.
The resolution in "Prisoner of Azkaban" marks a significant turning point in the series, leaving Harry with a newfound understanding of his past and a deeper connection to his family, particularly with Sirius Black. It also sets the stage for future adventures and challenges that Harry will face in the years to come.