Chapter 6 - "Talons and Tea Leaves" - In which students begin the new year of classes, Hermione is taking a very full course load and in Divination, Professor Trelawney predicts Harry's death. Hagrid introduces hippogriffs at his first class, Buckbeak is insulted, Malfoy is injured, and HRH go to console Hagrid.

At breakfast, Malfoy continues to mock Harry, and the students get their new course schedules - including Hermione, who is taking multiple courses simultaneously.
The Grim in the Teacup
Rushing off to the North Tower for Divination, Harry, Ron, and Hermione get completely lost. However, they run into Sir Cadogan, a loony portrait who guides them to the right place.
Harry, Ron, and Hermione climb the ladder into the Divination classroom, and get an extraordinary introduction to the class from Professor Trelawney. After several slightly eerie predictions, she sets the class to work reading tea leaves.
The Divination class sets out to try to read tea leaves, mostly without much success. Soon, though, Professor Trelawney takes Harry's cup - and promptly predicts his demise before dismissing the class.
Harry, upset over Professor Trelawney's prediction of his death, heads to Transfiguration. There Professor McGonagall tells him that Professor Trelawney predicts the death of one student every year, with no success.
At lunch Harry discusses the Grim and admits that he's seen a big dog, terrifying Ron and drawing annoyance from Hermione. Finally, when Ron accuses her of not having the right aura, Hermione storms off.
Hagrid Teaches His Very First Care of Magical Creatures Lesson
Harry, Ron, and Hermione make their way down to their first Care of Magical Creatures class. There, Hagrid tells the class how to open [The Monster Book of Monsters], despite snide remarks from Malfoy, and brings out a group of Hippogriffs to introduce them to the class.
Harry volunteers to go first with a Hippogriff, named Buckbeak. He carefully bows, then moves closer, and finally pets him - when Hagrid promptly has Harry climb on him and ride him around the paddock, returning to cheers from his classmates.
With Harry done for now, the rest of the Care of Magical Creatures class approaches the Hippogriffs - until Malfoy insults Buckbeak, prompting an attack, and Hagrid dismisses the class.