Readers of Harry Potter and the Half-Blood Prince were dismayed by the apparent death of Albus Dumbledore, Headmaster of Hogwarts, Chief Mugwump of the International Confederation of Wizards, and Chief Warlock of the Wizengamot. He is a crucial character in the Harry Potter books and in the development of Harry Potter himself. The wizard seems to have an unerring instinct for sources of danger, and wisely guides the other characters through perilous situations.
Dumbledore's death scene on top of the astronomy tower and subsequent funeral did leave many readers wondering if he was actually, in fact, dead. Many readers feel that a wizard with the strength and powers of Dumbledore could not possibly be killed, and may be faking his own death for reasons of his own which would become apparent in the next book, Harry Potter and the Deathly Hallows. Much to the disappointment of readers, J.K. Rowling has said that Dumbledore is in fact dead. Since he has mentioned that “to the well organized wizard, death is but the next great adventure,” perhaps his death is not as awful as readers think it is.
The death scene clearly suggests that Dumbledore did, in fact, die. The primary evidence for this is that the spell which bound Harry Potter into place was released when Dumbledore fell from the tower. Given existing evidence about how spells work, Dumbledore would had to have died for the spell to be lifted, unless another character, such as Severus Snape, knew that Harry was on the tower and performed a non-verbal spell to release him to trick Harry, and readers, into thinking that the wizard is dead. Furthermore, when Harry enters the headmaster's office after his apparent death, Dumbledore has appeared in the portraits of headmasters past, who presumably are all dead.
Some readers have argued that Dumbledore consumed the Draught of Living Death, which made him appear to be dead. During the climactic scene at his funeral when Fawkes, his phoenix, flies overhead and his tomb catches fire, perhaps Dumbledore escaped with Fawkes to safety. The fact that his tomb changes shape, concealing the evidence of a body, does lend credence to this theory. When this was brought up with Rowling, she merely repeated that Dumbledore was truly dead. Since she seems unlikely to allow his body to be used as an Inferius, one can assume that his body is inside his tomb.
What Rowling did not say whether or not Dumbledore would come back in the final book. Previous books have shown that the portraits of famous witches and wizards seem to have a bit of their spirit as well. In those books, readers have seen the wizards in the portraits offering advice or spying on remote locations through other portraits of themselves. The portraits are not quite ghosts, yet not quite alive, either. It seems probable that Dumbledore will speak to characters through his portrait, perhaps offering guidance and suggestions, just as he did of old, although he will not be able to physically assist Harry in his quest to defeat Voldemort. Some readers are also hoping that they will find out what Dumbledore sees in the Mirror of Erised, as most suspect that it is not, in fact, socks.