Harry Potter and the Half-Blood Prince

Further information: Plot of the novel
Lord Voldemort is tightening his grip on both the wizarding and Muggle worlds and has chosen Draco Malfoy to carry out a secret mission. Severus Snape makes an Unbreakable Vow with Draco's mother, Narcissa, to protect Draco and fulfill the assignment if he fails.
16-year-old Harry accompanies Albus Dumbledore to visit former Potions professor Horace Slughorn, who has gone into hiding but agrees to return to teach at Hogwarts. Dumbledore then takes Harry to the Burrow, where Harry reunites with his best friends Ron Weasley and Hermione Granger. Harry believes Voldemort has made Draco a Death Eater, after seeing Draco taking part in a ceremony, but Ron and Hermione are skeptical. At Hogwarts, Harry and Ron are forced to borrow textbooks for Slughorn's Potions class, and Harry is stuck with a copy that turns out to be filled with helpful notes, instructions, and spells left by the book's previous owner, the "Half-Blood Prince". Using the book, Harry excels in the class and impresses Slughorn. Ron becomes Keeper of the Gryffindor Quidditch team and forms a romantic relationship with Lavender Brown, upsetting Hermione. Harry consoles Hermione, revealing that he now has feelings for Ron's younger sister, Ginny Weasley.
Harry spends the Christmas holidays with the Weasleys. On Christmas Eve, Bellatrix Lestrange and Fenrir Greyback set fire to the Burrow. Back at school, Ron is nearly killed when he drinks poisoned mead, a drink originally intended for Dumbledore. While recovering, Ron murmurs Hermione's name, causing Lavender to end their relationship. Harry confronts Draco and severely injures him with a Sectumsempra curse taken from the textbook of the Half-Blood Prince. Snape enters and quickly heals Draco's wound. Fearing the book may be filled with more Dark Magic, Ginny and Harry hide it in the Room of Requirement and share their first kiss.
Dumbledore shows Harry memories of a young Tom Riddle and reveals that Slughorn retains a memory critical to Voldemort's defeat. Harry eventually succeeds in retrieving the memory, and learns that Voldemort wanted information for creating Horcruxes, objects that contain pieces of his soul. In the memory, Tom asked if dividing his soul into seven pieces was possible. Dumbledore concludes that Voldemort eventually did this, and two of his Horcruxes have already been destroyed: Tom Riddle's diary and his mother's ring. After discovering the possible location of another Horcrux, Harry and Dumbledore travel to a seaside cave where Harry is forced to make Dumbledore drink a painful potion that hides the Horcrux, Slytheerin's locket. A weakened Dumbledore defends them from Inferi and apparates back to Hogwarts, where Bellatrix, Greyback and more Death Eaters have entered with Draco's help through a Vanishing Cabinet.
Dumbledore instructs Harry to hide as Draco arrives, disarms Dumbledore and reveals that he has been chosen by Voldemort to kill the headmaster. However, he is unable to bring himself to do it, and Snape casts the Avada Kedavra curse instead, killing Dumbledore. Harry attempts to curse Snape, but Snape overpowers him and reveals that he is the Half-Blood Prince. Harry returns to the school to find the staff and students mourning Dumbledore. Harry later reveals to Ron and Hermione that the locket Horcrux was a fake. The locket contains a message from "R.A.B.", stating that he has stolen the real Horcrux with the intent of destroying it. Rather than return for their final year at Hogwarts, Harry, Ron and Hermione vow to seek out and destroy the remaining Horcruxes.

Question: What curse does Snape use to kill Dumbledore?
Answer: Avada Kedavra