Harry Potter and the Half-Blood Prince begins with the Minister of Magic speaking to the Prime Minister of Britain, and we learn some new things about the universe they live in. So during the introduction, we see nothing through Harry's point of view (because he's not present). It is mostly through the Prime Minister's point of view (sort of, these books are in third person). The new Minister of Magic, Rufus Scrimgeour, informs the Prime Minister of a returning threat, Voldemort. Scrimgeour also explains to minister that him, the minister, has had security put with him. To which, the Prime Minister is rather displeased by, as he had not requested it. So they speak of a few other things, and then Scrimgeour leaves.

In the last two Harry Potter books, Rowling had begun with Snape and telling us some information, but not all. She had done this to keep the reader intrigued to find out if Snape was actually with Voldemort. And, in the case with the Half-Blood Prince, to inform us on something that had changed ( i.e. new minister). It allows the reader to know something that Harry does not, which is new to these books.

In the introduction, after Harry gets to Hogwarts, he gets a pre-owned potion book since he had not bought one and it had extra advice from someone who had called himself "The Half-Blood Prince". The notes made him very good at potions and the best in the class.

During the rising action, Harry learns about the horcruxes and that he must destroy them, in which Dumbledore tracks one down (well, we learn that it had already been taken by someone, but that's in the next book). He learns of them after Dumbledore showed him a memory that Slughorn (a professor) had lent him, but the memory had the most important parts blurred and edited. Harry's mission was to acquire the complete memory from Slughorn and Harry does so by getting Slughorn drunk.

I believe that the story was written well and that the plot twist worked as it was intended. It left with a lot of questions, which are answered in the next book. It was enjoyable and (mostly) consistent. My one problem which is a plot hole is when Dumbledore tells Harry that making a horcrux requires killing an important person, and since Voldemort had made several he killed multiple. The problem is when Dumbledore tells Harry the people Voldemort killed, the last one he lists is "a random muggle man" which is most definitely not an important person. But other than that I have no gripes.