The sixth book in the Harry Potter Series "Harry Potter and the Half-blood Prince" is in many ways Harry Potter's final lessons. After this book he is not longer a student but instead a soldier. Dumbledore seems to recognize this as he finally begins to take Harry Potter into his confidence, teaching and interacting with Harry directly far more than he has in previous books.
Much of the connection and examination of Dumbledore come in the use of his pensive. A magical memory catching device that allows both Harry and Dumbledore to enter into memories most of which show them about Voldemort. One of the things that these reveal is that Voldemort has become nearly immortal due to his use of horcruxes. These use the soul shattering experience of murder using magic to separate and store a portion of Voldemort's soul. He has done this six times. So long as they exist Voldemort can not die. Harry has already destroyed one of these, the diary of Tom Riddle that was the major danger in "Harry Potter and the Chamber of Secrets" and Dumbledore has destroyed another.
In addition to Dumbledore's connection with Harry Snape takes an even more central role in this book. Early in this book Snape makes an unbreakable vow to Draco Malfoy's mother to protect her son and do the job for him. In addition to this Snape is made the new defense against the Dark arts teacher, a job he has wanted for years but has always been turned down for.
With many deaths in the Harry Potter books the one at the end of this book is the memorable. One of the reasons that I believe that this is such an important moment in the book, besides the obvious is that it is out of Harry Potter's control. This is an event that Harry doesn't really cause and he is powerless to stop and yet it defines much of the rest of his life. It is this type of death that is rarely seen in fiction yet is the most common in the real world.
As much of the rest of the series examines how Harry Potter grows up to be a good person this book largely does the reverse showing not how Harry Potter became the person he is but how Tom Riddle became Voldemort. This allows the author to examine the same themes of her book from a new direction.
While as much fun and well written as the other books this is a book that could be difficult for many of the readers of the Harry Potter Series. These are books that are meant to be read by people the same age as the characters and as the characters get older the books reflect that more so be aware that this is a book for those nearing adulthood and written as such.