Chapter 18 - "Birthday Surprises" - In which Harry gives Slughorn a bezoar instead of an antidote in Potions class, then asks him unsuccessfully about Horcruxes. The sixth-years then have their first apparition lesson, where Harry overhears Malfoy saying Crabbe has been acting as his lookout, and Harry starts watching the Marauder's Map. Then, on Ron's birthday, Ron accidentally consumes Romilda Vane's love potion and Harry takes him to Slughorn to get an antidote; there, Slughorn gives Ron some poisoned mead and Harry saves his life with a bezoar.

Harry discusses his new homework for [Dumbledore] - obtaining the memory from Slughorn - first with Ron and then with Hermione.
The Bezoar Solution
In Potions class, Professor Slughorn assigns students to brew antidotes to poisons, which excites Hermione because Harry won't be able to get help from the Half-Blood Prince.
Without the help of the Half-Blood Prince, Harry is unsuccessful in brewing an antidote to his poison. However, at the end of the lesson, he presents Slughorn with a bezoar instead - delighting Slughorn and infuriating both Ron and Hermione.
After Potions class, Harry stays back to ask Slughorn about Horcruxes - but Slughorn gets upset and storms off.
Harry tells Ron and Hermione about his failure to retrieve the memory from Slughorn, but they are unsympathetic thanks to his triumph with the bezoar in Potions class.
As time passes, Professor Slughorn stops issuing Slug Club invitations, but otherwise resumes his normal glowing treatment of Harry.
Hermione gets frustrated when, for the first time Harry can remember, she is unable to find something in the Hogwarts library - the definition of a Horcrux.
The Apparition Lesson
The sixth years have their first [Apparition] lesson with [Wilkie Twycross] in the Great Hall. Harry overhears Draco arguing with Crabbe, but other than that and Susan Bones's [splinching], nothing interesting happens.
After overhearing Malfoy and Crabbe during [Apparition] lessons, Harry is convinced that Malfoy is using Crabbe and Goyle as lookouts - but he doesn't know for what - and he and Ron run up to their [dormitory] to look for them on the Marauder's Map.