The third Harry Potter book. I think it's my favorite though I will recheck after I finish this re-read of all of them.
News of an escaped prisoner, a murderer named Sirius Black, is on TV. In his own life, Harry learns that he needs a permission slip signed to escape Hogwarts for the nearby town, where the third-years are sometimes allowed to go. He manages to strike a deal with his uncle, but when "Aunt Marge" -- Dudley's aunt, and as nasty as the rest of the family -- spends a week and starts insulting his mother, he finally blows his stack and blows her up like a balloon. Literally. Violating a lot of restriction on under-age wizardry. So he runs off.
Some adventures later, having found out that Sirius is a wizard so dangerous they warned the Muggles, too, Harry finds the Minister of Magic himself drawing him into Diagon Alley and downplaying the notion that his magic was serious. Harry, bewildered, hangs out in the alley for a time, learns the murdered before connecting with Ron and Hermione -- Hermione gets a cat -- and going to the Weasleys, where he overhears Mr. Weasley thinks he should be told that he has a connection to Sirius , and should be warned. Just before they get on the train, Mr. Weasley corners him to warn him, and having heard Harry knows already, adds that he must never go after Sirius himself.
And they arrive at Hogwarts to find the monstrous dementors are keeping watch for fear of Sirius reaching the school. The new Defense Against Dark Arts wizard stops them when they endanger some of the students.
He proves to be a cool teacher. The plot, which is one of the most elegant and detailed, also involves James Potter's school friends, a haunted shack, Fred and George giving Harry means to get to the village without the permission slip, an unexpected Christmas present, Hagrid sagely advising Harry and Ron that some people don't think quite straight about their pets, a magical protection from dementors, and more.
[Spoiler (click to open)]I must confess that after Snape was the Obviously Guilty Person in Stone, and Malfoy in Chamber, I never really seriously considered that Black wasn't innocent, somehow. Ah, the perils of reusing tropes. Still liked the story and found the specific exoneration interesting.