LitCharts assigns a color and icon to each theme in Harry Potter and the Prisoner of Azkaban, which you can use to track the themes throughout the work.
Justice
Storytelling and Perspective
Teaching
Responsibility, Morality, and Time
Friendship and Growing Up
Summary
Analysis
Hermione offers Harry the note from Hagrid. It's spotted with tears and reads that Buckbeak's execution date hasn't been decided yet. Hermione says that Lucius Malfoy scared the Committee into it, and Ron promises to help with Buckbeak's appeal. At this, Hermione throws her arms around Ron's neck and apologizes about Scabbers.
It's telling that Ron and Hermione make up after they're forced into shifting their attention to another of their friends. This shows that friendship, in all forms, can be used to encourage other friends to make up and think better of each other.
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Quotes
Harry, Ron, and Hermione can only talk to Hagrid during Care of Magical Creatures, as security measures don't allow them out of the castle in the evenings. One day after class, Hagrid cries. As the trio walks up to the castle, they see Malfoy, Crabbe, and Goyle inside the castle doors, laughing at Hagrid. Hermione slaps Malfoy across the face and berates him. Terrified, Malfoy runs, and Hermione tells Harry that Gryffindor has to win the Quidditch final against Slytherin. They head to Charms but as Ron and Harry arrive, they realize that Hermione is gone. She doesn't turn up all class and misses the lesson on Cheering Charms.
Hermione's absence for Cheering Charms suggests that the responsibility of having to remember her schedule and move back and forth through time is starting to negatively affect her life. Especially when her compromised mental health seems to instigate her hitting Malfoy, it suggests that there are major consequences to using time travel for personal gain.
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After lunch, Harry and Ron find Hermione asleep on an Arithmancy book in the common room. She's distraught when she realizes she "forgot" to go to Charms, and Ron tells her that she's doing too much. A bit later she joins the boys for Divination and they sit at a table around a crystal ball. Trelawney greets the class and says that "the fates have informed her" that they need to start crystal balls early, since they'll be on the exam. Hermione snorts that Trelawney writes the exam, but Trelawney ignores her.
Because Hermione is able to manipulate time herself, she doesn't take Trelawney's predictions at all seriously. Hermione has the privilege of seeing how multiple things play out because she actually is in multiple places at once, and the fact that she takes time travel so seriously makes it seem as though Trelawney's frivolous predictions aren't worth her time.
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As Harry, Ron, and Hermione look at their ball, Hermione hisses that she'd be better off using this time to learn Cheering Charms. Ron jokes that the foggy crystal ball means that there's going to be fog tonight, which makes Harry and Hermione laugh. Trelawney reprimands them and then sits down at their table and breathily says that she sees the Grim in Harry's ball. When Hermione deems this ridiculous, Trelawney angrily tells Hermione that her mind is "hopelessly mundane." Hermione packs up her things and leaves. Lavender reminds Trelawney that she predicted someone would leave around Easter.
Though in some ways, Trelawney is doing Hermione a favor by basically encouraging her to drop the class—Hermione clearly doesn't like it and finds it a waste of time—it's also worth noting that saying things like this to students isn't entirely appropriate. This moment begins to shift Trelawney more in the direction of Professor Snape and his outright favoritism.
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The Easter holidays are barely a holiday with everyone's exam preparations. Ron works on Buckbeak's appeal in his spare time, while Harry has Quidditch practice every evening. Oliver reminds Harry constantly that in the coming match against Slytherin, he can't catch the Snitch unless Gryffindor is ahead by at least 50 points.
Ron's choice to take over research for Buckbeak’s appeal shows that now that he understands his friendships with Hermione and Hagrid are more important than anything else, he can show them this by putting in the work and following through on his promises.
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Harry has several bad dreams two nights before the match and finally wakes up before dawn. He goes to the window and sees Crookshanks on the lawn with the huge black dog. Harry tries to wake Ron and wonders if the dog is actually an omen if Crookshanks can also see it.
Seeing Crookshanks with the dog suggests that the dog is real—it's not just a vision. In this way, Crookshanks starts to act as a voice of reason and as a test for what Harry should take seriously or not.
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The morning of the match, Ravenclaws and Hufflepuffs wish Harry good luck. The Gryffindor team steps onto the field. Madam Hooch sends the players off and the game immediately turns dirty. Slytherins crash into Gryffindor players, and Fred throws his Beater's club at a Slytherin player. Madam Hooch awards a number of penalties and Gryffindor's lead grows. Harry sees the Snitch and races for it, but Malfoy grabs the Firebolt's tail and slows Harry down. Several Slytherin players converge on Angelina, so Harry flies at them and scatters them all. However, when he turns his attention back to Malfoy, he sees that Malfoy is diving for the Snitch. Harry chases him, knocks Malfoy's arm aside, and catches the Snitch. The Gryffindor supporters scream, and Gryffindor wins the Quidditch Cup.
The fact that both Gryffindor and Slytherin players play dirty during this game shows that though the Gryffindors are cast as the "good guys" throughout the series, they're not above meeting the Slytherins at their level. In other words, the tenor of this match humanizes both teams and shows that they all just want to win the Cup. Madam Hooch's penalties are an attempt to create a sense of justice and fairness for a game that, to an outside observer, looks as though it isn't fair at all.