Helping Hagrid Feel Better
Sitting in Hagrid's hut, the trio discusses Care of Magical Creatures with Hagrid, who admits he's also partially upset because Aragog is close to death. After Hermione offers to help and they all assure Hagrid that he's a good teacher, they depart, leaving him more cheerful.
Sitting at dinner, Hermione reads that Arthur Weasley has raided the [Malfoy mansion], Harry tries again to sell his theory that Malfoy is a Death Eater, and [Demelza Robins] arrives to tell Harry that Snape won't let him out of his detention.
Chapter 12 - "Silver and Opals" - In which Harry tries one of the Half-Blood Prince's spells while reading in bed and levitates Ron by accident, argues with Hermione over the danger of the Prince, and gets word of his next lesson with Dumbledore. The trio then walks to Hogsmeade, where Slughorn corners Harry in Honeydukes and Harry sees Mundungus with things stolen from Grimmauld Place. On the way home, an Imperiused Katie Bell touches a cursed necklace and is hurt; Harry then suspects Draco and tells McGonagall this, though Ron and Hermione don't believe him.
Unable to figure out why [Dumbledore] has been disappearing so much, Harry feels slightly abandoned that his lessons haven't continued.