This is book number six in the Harry Potter series that was written by J K Rowling and in this particular story the Headmaster of Hogwarts School (Albus Dumbledore) has come to collect Harry at Privet Drive. The Dursleys then had an uncomfortable few minutes before Harry left with his Headmaster.

As even though Albus was trying to be polite by offering the Dursleys drinks they wouldn’t accept them, and he also would’ve noticed that they were terrified of him. Though, Albus Dumbledore wasn’t going to let the opportunity go to waste:

When he told the Dursleys what he thought of their treatment towards Harry.

Albus Dumbledore even dared to say that Harry’s cousin Dudley was also mistreated. Then Harry and his Headmaster went to where Albus Dumbledore knew where Horace Slughorn was staying as Albus knew that:

Harry’s ambition was to become an Auror when he left school.

Albus also knew that Professor Severus Snape accepted only Outstanding in his O.W.L. classes. So, Albus Dumbledore knew that he had to try to persuade Horace to return. As Horace accepted a lower grade for Potions.

However, Harry and Ron return to Hogwarts School a bit unprepared. As they both thought that they wouldn’t be able to study Potions this year. So, as Harry and Ron didn’t have this year’s potions textbooks, they both received old copies.

Harry was given the copy that the Half-Blood Prince had wrote in and I think that this was done perhaps on purpose. As nobody knew who the Half-Blood Prince was accept Albus Dumbledore and Albus Dumbledore was giving Harry private lessons: and his reason was because he needed to explain and show his memories to Harry so that he’ll understand as one big advantage in Harry’s favor was that Professor Dumbledore taught Lord Voldermort. Professor Dumbledore also had advised Harry to only talk about the things he shows and discusses with Ron and Hermione.

He also advised Harry too, that he should tell Ron and Hermione that they weren’t to talk about what Harry tells them about his private lessons with anyone but him.

As perhaps Albus knew that there were people that wouldn’t approve? Also, he didn’t want Lord Voldermort to discover too soon: that they had worked out what he had managed to do and had succeeded in keeping it a secret for so long.