Chapters Six, Seven, and Eight in Harry Potter and the Sorcerer's Stone by J.K. Rowling provide exposition into the world of Hogwarts. These chapters are pivotal to the whole series, because they introduce the most important characters of the novel and the rest of the series, for that matter.
Chapter Six takes place at King's Cross. Harry sees the Weasley family for the first time and boards the train for Hogwarts. On board the train, he ends up sitting with Ron Weasley. He sees Draco Malfoy again and meets Hermione Granger for the first time when she pops in to ask if they had seen Neville's toad.
Chapter Seven gives the reader the first glimpse of Hogwarts and reveals a cast of characters that would be Harry's future teachers and classmates. At the sorting, a variety of Harry's fellow students are sorted, and Harry sees Snape looking harshly at him for the first time. Dumbledore provides a whimsical speech and warns students not to go to the forbidden forest.
Chapter Eight: No new characters are introduced, except Fang, Hagrid's dog. Harry goes to Hagrid's hut for tea. He also has a wretched first class with Professor Snape. Hermione and Ron as well as other fellow students are with Harry in class, including the Slytherin house first years.
The main characters in chapter 6 are significant in that this is Harry's first encounter with the Weasley family. He meets the twins, Fred and George, and Ron Weasley. He comes into contact with Hermione Granger and Draco Malfoy on the train.
In chapter 7, the group is greeted by Professor McGonagall. Each new student is sorted into halls by the "Sorting Hat". Harry meets Sir Nicolas de Mimsy-Porpington, the resident ghost of Griffindor. He meets Neville, Professor Snape and Albus Dumbledore, as well.
In chapter 8, Harry, Ron, and Hagrid are the main characters along with Hagrid's dog Fang playing a smaller role.