The summaries below give a brief overview of the chapters when Harry arrives at Hogwarts and the First Task of the Triwizard Tournament. Here Durmstrang and Beaxbatons come to Hogwarts, Harry is selected as one of the school champions, and he completes the First Task.
In Chapter 11, Harry and his friends leave the Weasleys' house for the Hogwarts Express, meeting several people on it and finally arriving at Hogwarts. In Chapter 12, after everyone at Hogwarts finished eating the start-of-term banquet, the new Defense Against the Dark Arts teacher arrives, Professor Moody. Dumbledore also informs everyone that the Triwizard Tournament will be played at Hogwarts that year and explains all about it. Everyone immediately wants to sign up, including Harry himself.
In Chapter 13, Harry and his friends start their classes at Hogwarts. When Draco Malfoy starts insulting Ron about his family and then attempts to curse Harry behind his back, Professor Moody immediately steps in and transfigures Malfoy into a ferret, amazing everyone. The rest of the chapter is then devoted to talking about him and how cool he is considered amongst the students of Hogwarts. Similarly, most of Chapter 14 talks about Professor Moody, too, including the first class Harry has with him. Later in the chapter, Harry receives a note from Sirius that he is flying North to be closer to Harry should something suspicious like his scar hurting again happen.
In Chapter 15, the two other wizarding schools competing in the Triwizard Tournament arrive at Hogwarts; Durmstrang and Beauxbatons. As an interesting surprise, Victor Krum, one of the Quidditch players that Harry and Ron saw at the World Cup, was a seventh-year at Durmstrang. In Chapter 16, the three wizarding schools eat a feast together and Dumbledore explains how the Goblet of Fire will work. The next day, when the Goblet of Fire made its decision, four names came out… one of them being Harry’s, even though he was an underage wizard!
In Chapter 17, Harry joins the other three champions in the chamber off of the great hall in immense astonishment and confusion. All of the professors and ministry workers debate the subject and realize that Harry is forced to compete, as his name coming out of the goblet creates a binding magical contract. When Harry arrives at the Gryffindor common room, he is greeted by intense celebration, (as everyone was very proud of Harry becoming a champion and bringing even more fame to their house Gryffindor), but also demanding answers to how he supposedly cheated his way into the tournament. Even worse, Harry’s best friend, Ron, doesn’t believe that Harry didn’t cheat, and the two become angry at each other, their friendship weakening. In Chapter 18, Harry goes through difficult times as everyone at Hogwarts is furious at him for entering the tournament. He also meets Rita Skeeter, a journalist for the Daily Prophet who will be important later on in the book.
In Chapter 19, Hagrid secretly shows Harry the dragons that he will soon have to face during the first task, allowing him to be forewarned about the difficulty and seemingly impossible nature of the task. Very soon after, he talks to Sirius through the fire in the common room, who warns Harry about being careful and watching out for Karkaroff, fire. a past supporter of Voldemort who might have been the one who tricked the Goblet of Fire into picking Harry. In Chapter 20, Harry faces the First Task and is surprisingly successful. He then regains his friendship with Ron, who finally believes that Harry didn’t volunteer for the tournament after seeing the sheer difficulty and how dangerous it was for Harry.