The next morning, Harry writes a short letter to Sirius insisting that it's unnecessary for him to return. He takes it to Hedwig in the Owlery and sends her off, and tells Hermione and Ron about what he did at breakfast. Harry tries not to worry over the next few weeks, though this is made easier by how hard he has to work at his lessons. One day, Moody announces that he's going to put the Imperius Curse on everyone in turn so they can practice resisting. Hermione tries to insist that it's not legal, but she backs down. When it's Harry's turn, Moody tells him to jump on a desk. Harry successfully resists the curse after a few tries.
Here, Hermione finds herself caught between going against a teacher and going against the rules, something that forces her to examine exactly what she wants to get out of this lesson. When she agrees to go along with Moody's lesson, it suggests that she's learning to trust individuals like Moody rather than blindly following the rules of large entities like the Ministry.
McGonagall explains to the students that they're approaching the time when they'll take their Ordinary Wizarding Levels and need to be prepared. Most of the class is aghast, as they don't take their O.W.L.s until the end of their fifth year. Snape assigns work on antidotes and hints that he's going to poison a student soon to test them, while Professor Flitwick assigns extra reading on Summoning Charms. Hagrid asks students to come down in the evenings to observe the skrewts, which are growing despite not eating anything, and he reminds Malfoy that he makes a great ferret when Malfoy tries to refuse.
By bringing up the O.W.L.s, McGonagall tries to impress upon her students that the future is coming faster than they think it is, and that what they're learning in school right now is actually very important. On a more series-level scale, this indicates that everything students learn at Hogwarts will in theory prepare them for life in the adult Wizarding world; there are no "just for fun" classes and test results are very important.
In the entrance hall one night, Ron reads an announcement about the Triwizard Tournament over the heads of other students crowded around. It says that on October 30, lessons will end early so that students can greet the guests from Durmstrang and Beauxbatons. Harry is thrilled, as this means that Snape won't be able to poison them. They hear a Hufflepuff student running off to tell Cedric and Ron expresses derision that Cedric is going to try to become the Hogwarts champion. Over the next week, rumors abound and the castle undergoes a thorough cleaning.
Ron's derisive comments about Cedric suggests that he's very invested in maintaining a sense of difference between the different Hogwarts Houses--at this point, Ron doesn't see a possible victory for Cedric as a victory for him too, though their loyalty is to the same school. This shows that anyone, even Ron, can cling to these divisions in a way that makes him less empathetic towards others.
At breakfast on the morning of the 30th, Harry, Ron, and Hermione notice Fred and George sitting away from everyone else. The trio hears George saying that if "he" won't talk to them, they'll have to send a letter. Fred and George refuse to share who and what they're talking about, so Harry changes the subject to ask if the twins have thought more about how to enter. They haven't, but the boys all discuss the tasks and the judging. Hermione interjects that three of the judges will be school headmasters, according to Hogwarts: A History. She suggests that the book should actually be called A Revised History of Hogwarts and hisses that it makes no mention of house-elves.
When Hermione begins suggesting other names for Hogwarts: A History that make it clear the text is biased and represents the perspective of only one person, it shows that she now understands that she can't take everything she reads at face value. Instead, she needs to go forward understanding that it's necessary to critically evaluate books for bias and authorial intent, but that having to do so doesn't mean that books aren't useful.
Harry shakes his head and returns to his breakfast. Both he and Ron joined S.P.E.W. to appease Hermione but have remained unenthusiastic about the cause. Few others have joined. George asks Hermione if she's ever been to the kitchens and says that the elves there are happy. Hermione insists that the elves are brainwashed, but the argument dissolves when the post owls arrive. Hedwig brings Harry a letter from Sirius that says he's still coming back.
The text implies here that Hermione hasn't been to the kitchens, which indicates that she's waging war for house-elf liberation without having consulted the very beings she wants to support. This is Hermione's major oversight, as George makes a good point: S.P.E.W. is useless unless it does something the elves actually want.
When lessons end in the afternoon, the Heads of Houses organize the students into lines. McGonagall leads the Gryffindors outside to wait with the rest of the school. After a few minutes, Dumbledore calls that Beauxbatons is coming. Students point to the sky as a massive horse-drawn carriage soars toward them. The horses are as big as elephants. After the carriage lands, a boy unfurls stairs and an elegant woman as large as Hagrid steps out. Dumbledore leads the Hogwarts students in applause and greets the woman, whom he calls Madame Maxime. She leads her shivering students inside.
The fact that Madame Maxime is the headmistress of a renowned Wizarding school shows that not everyone of Hagrid's size needs to be relegated to the role of gamekeeper; it seems that Maxime is a competent witch.
A few minutes later, Lee Jordan points to the lake. A huge ship rises up from the depths. All the Durmstrang students seem bulky, but Harry realizes that this is because they're wearing fur cloaks. The headmaster, Karkaroff, greets Dumbledore and leads his student Viktor inside first, as he has a cold. Ron hisses that "Viktor" is Viktor Krum.
The realization that Viktor Krum is still a student helps to bring him down a little from his celebrity and make him more relatable for fans like Harry and Ron. In other words, the fact that Krum is in the same boat as they are makes him easier to empathize with.