Chapter 9 - "The Midnight Duel" - In which Gryffindor and Slytherin have flying lessons together, Neville injures himself on his broom, and Harry and Draco fight it out on brooms over Neville's Remembrall, resulting in Harry being made Seeker of the Gryffindor Quidditch team. Later, Draco challenges Harry to a wizard's duel, but instead of dueling he tells Filch in hopes of Harry being caught and expelled. Harry and his friends evade Filch and after encountering Fluffy, the three-headed dog, are safely back in their dormitory.

The Start of Harry's First Year
Despite high expectations, Harry and his classmates are disappointed by a disappointing first Defence Against the Dark Arts class with Professor Quirrell.
As his first week progresses Harry realizes he isn't really behind the other first years.
Sitting at breakfast Friday morning, Harry and Ron discuss Snape and McGonagall, and Harry gets a note inviting him to visit Hagrid in the afternoon.
The first years descend to the dungeons for their first Potions class, in which Snape belittles Harry almost instantly and takes several points from him for irrelevant things.
Harry and Ron head down to visit Hagrid, where they discuss Snape's hatred of Harry and ask Hagrid about the break-in at [Gringotts].
Flying Lesson
The Gryffindors learn that they will be having flying lessons with the Slytherins, and sit at breakfast discussing their nervousness. Neville also gets a package from home with a Remembrall, which Malfoy briefly snatches from him.
The Gryffindors and Slytherins begin their first flying lesson, and just as they're beginning Neville falls and breaks his wrist, prompting Madam Hooch to take him off to the hospital wing with strict warnings to the others to stay off the [broomsticks].
With no teachers around, Draco Malfoy grabs Neville's Remembrall and flies up in the air with it. Harry chases after, despite warnings from classmates - and when Malfoy throws it, makes a magnificent diving catch.
After spotting Harry flying after the Remembrall, Professor McGonagall calls him down and leads him inside, stopping to ask Professor Flitwick if she could take [Oliver Wood] out of class as well.