Muggles are beginning to notice signs of the war spilling over from freak accidents and whatnot. The book opens with the Prime Minister (not specifically Tony Blair) meeting with the sacked Minister of Magic Cornelius Fudge and the new Minister of Magic Rufus Scrimgeour and talking about Voldemort.
We also see Black sisters Bellatrix Lestrange and Narcissa Malfoy visit Hogwarts Potions teacher Severus Snape, where Narcissa makes Snape take an unbreakable vow (you die if you break it) that he will help her son, Draco, in a task he is about to go on (it is unclear what Draco is doing).
Harry is first seen in the third chapter, when Dumbledore comes to Privet Drive to escort Harry to the Weasley's house. First they stop at the hiding place of a friend of Dumbledore's, Horace Slughorn, where Harry almost accidentally convinces Slughorn to come to teach at Hogwarts. (We assume this is for the vacant Defense Against Dark Arts post).
Dumbledore tells Harry that he will be giving him private lessons of a sort and advises him to tell Ron and Hermione about the prophecy.
At the Weasleys' Harry tells his friends about the prophecy, and receives his OWLs (a sort of standardized test). He doesn't think he can get into Potions because he is one grade short of what Snape, the potions master, accepts. Harry also learns that Fleur Delacour (from Goblet of Fire) is engaged to Ron's brother, Bill.
While the trio visit Diagon Alley to purchase robes and supplies, the meet Draco Malfoy and by an action of his (pulling his arm away), Harry guesses that Draco has been branded a Death Eater (A follower of the bad-guy Lord Voldemort). They follow Draco to a dark shop, Burgin and Burkes where he says something about "keeping that one safe" (important) and asks how to repair something.
When they arrive at Hogwarts, Harry is shocked to learn that Slughorn will be teaching Potions, not Defense Against Dark Arts, and (his loathed teacher) Snape will be teaching the Defense Against Dark Arts course. This means, however, that Harry can take the Advanced Potions course, but because he was not expecting it, he has no books and has to borrow one from Slughorn. Inside are additional potions tips and spells which put Harry at the top of the Class. These tips are from an elusive "Half-Blood Prince."
The lessons with Dumbledore turn out to be looking into Pensieve memories, where Harry learns more about Voldemort's past, especially his mother, Merope Gaunt, a basically powerless and abused witch who uses magic to force muggle (not wizard) Tom Riddle to marry her. We also see Dumbledore telling young Voldemort (called Tom) that he is a wizard and we see that Voldemort was one creepy little kid. We also learn that Voldemort likes to collect things which Dumbledore says is important.
A fellow student of Harry's, Katie Bell, gets cursed by an opal necklace that she is force to pick up by the Imperius curse (it makes you do things against your will) while away from the school. Harry suspects Draco Malfoy, but he has an alibi. Harry starts learning many hexes and spells from his potions book (the Half-Blood Prince).
Just before Christmas, Harry overhears Draco Malfoy and Snape talking about the help Snape promised Malfoy in the unbreakable vow. When Harry tells this to Remus Lupin (a former teacher and werewolf) and Mr. Weasley at Christmas in the Weasley's house, they both say that they trust Snape because Dumbledore does. Remus Lupin also tells Harry about Fenrir Greyback, the evil werewolf who bit him when he was a child (somewhat important). There is also something wrong with Nymphadora Tonks (another member of the Order of the Phoenix) which they suspect is due to her grief over her cousin Sirius (who died in the last book).
Harry looks inside the Potions textbook and sees that it is 50 years old, which he thinks eliminates his father and friends from being the Half-Blood Prince. Hermione does some research showing that the Half-Blood Prince could be anyone, even a girl, showing him something about a former Hogwarts student, Eileen Prince (kind of important).
In one of the lessons Dumbledore shows Harry about how young Voldemort covered killing his muggle (non-wizard) father and muggle grandparents (the Riddles) by pinning it on his wizard uncle (Morfin Gaunt). Dumbleore also shows Harry a memory where teenage Voldemort asks Slughorn about Horcruxes (we aren't told what these are), but the memory has obviously been altered by Slughorn. Dumbledore sets Harry on finding out what really happened. We also see how a younger Voldemort killed a woman to get a locket owned by Slytherin and a cup owned by Hufflepuff (founders of Hogwarts).
When Harry at first tries to interrogate Slughorn about the Horcrux, he refuses to talk, then at another opportunity Harry's friend Ron gets poisoned (Harry saves him) before Harry can ask. Finally Harry uses guilt about his mother (a favorite student of Slughorn's) to get the real memory.
In the real memory we learn that Horcruxes are divisions of the soul that can be created when a person murders someone. Voldemort, to be immortal, killed and divided his soul 6 times, so he has seven pieces of his soul around. One is a ring that Dumbledore had already found and destroyed. One was the destroyed Diary of young Voldemort from Chamber of Secrets, one is stored in Slytherin's Locket, and another in Hufflepuff's cup. Another is stored in Voldemort's serpent, Niagini, and Voldemort obviously has a piece of a soul inside him. Dumbledore does not know where the other one is stored, but he suspects that it is in an artifacts relating to Gryffindor or Ravenclaw (the other two founders of the school). This makes Voldemort immortal, because there are still places his spirit inhabits even after he has been physically destroyed. This is why Voldemort survived the rebounded curse when he tried to kill Harry the first time.
Dumbledore tells him that he has a choice to help him destroy the Horcruxes, and that he can choose to follow the prophecy or not. Dumbledore also tells Harry that the power he has that "the Dark Lord knows not" spoken of in the prophecy is love. Harry knows because he loves his friends, mentors, and dead parents, that he must fight Voldemort.
Harry's life continues, including his beginning to date his friend Ron's little sister, Ginny. Harry finds a spell in the Half-Blood Prince textbook labeled "For Enemies." Harry gets into a fight with Draco Malfoy and uses it on him, but it seriously injures Draco, causing large gashes and bleeding. Professor Snape finds them and heals this, sort of reads Harrys mind (Legimency), and then demands to see Harry's books, but Harry hides the Half-Blood Prince book in the a special room called the Room of Requirement behind a vanishing cabinet and shows him Rons instead (important).
Harry receives a message from Dumbledore that he has found out where a Horcrux is and to help him destroy it. On the way Harry meets up with the Divination teacher, Trelawney, who made the big prophecy about him. Trelawney tells him about a strange occurrence in the Room of Requirement, and Harry guesses that Draco has succeeded in whatever he was planning. From Trelawneys ranting, Harry realizes that the Death Eater who overheard the prophecy and told Voldemort about it (thus leading to Harry's parents' deaths) was Snape. Harry confronts Dumbledore, but Dumbledore insists that he trusts Snape and that Snape regretting bringing about Harry's Parents' Deaths. Dumbledore makes Harry promise he will follow any order given, and tells him to prepare for getting the Horcrux.
Before Harry leaves, he tells Ron and Hermione to round up their group (from Order of the Phoenix) and to watch Snape and the room of requirement. He then leaves with Dumbledore.
Harry and Dumbledore go to a cave by the sea (mentioned in one of the memories about young Voldemort). They go through this complex place to this pool where Dumbledore has to weaken himself by drinking a potion to get out a Horcrux, the locket. The potion weakens Dumbledore.
They return to Hogsmeade, and see a Dark Mark hanging over the Hogwarts castle. A Dark Mark is the symbol the Death Eaters that is usually sent up when they have murdered someone. Dumbledore and Harry fly to the Astronomy tower of the castle and prepare to enter when they hear someone approaching.
Dumbledore petrifies Harry while he is invisible to protect him, at the expense that Dumbledore (weakened still) is disarmed by Draco Malfoy. Dumbledore tries to talk Draco down, telling how Draco's earlier attempts to kill him were half-hearted (the necklace and the poison that Ron drank). Draco Malfoy reveals that he was able to bring Death Eaters into Hogwarts through a pair of vanishing cabinets (one in the room of Requirement, the other in the dark shop from the beginning of the book). Draco insists that he has to kill Dumbledore, otherwise Voldemort will murder his family. Dumbledore basically talks Draco down, but other Death Eaters show up, including the untransformed werewolf, Fenrir Greyback. The Death Eaters insist that Draco has to kill him, but then Snape shows up. Dumbledore appears to plead with Snape but Snape kills Dumbledore (the Avada Kedavra) and takes Draco away.
Harry chases after Snape and uses some of the spells he learned from the Half-Blood Prince book against Snape. Snape reveals that he is the Half-Blood Prince, and is able to deflect Harry's attacks. Snape prevents any of the other Death Eaters from killing Harry, but basically stuns him while the Death Eaters and he leave Hogwarts and disappear.
Man of the students wake up, and find Dumbledores body on the lawn (it fell from the tower when he was murdered). Harry finds the locket, but sees that it is fake. Inside is a letter from a mysterious R.A.B. to Voldemort saying that he/she/it had taken the Horcrux and would destroy is when he/she/it could, knowing that soon he/she/it will soon be dead. Harry is distraught that Dumbledore was weakened for nothing. Ginny comes and takes him to the hospital wing.
They go to the hospital wing, where most of the people who had been fighting the Death Eaters were. Lupin, Tonks, Bill Weasley and Professor McGonagall had been patrolling the corridors for Dumbledore, while Ginny Weasley, Luna Lovegood, Neville Longbottom, Hermione Granger, and Ron Weasley had been on alert from Harry.
The only one seriously hurt, Bill, was practically mauled by the Fenrir Greyback and though he was not transformed (yeah, Fenrir is very creepy). Lupin speculates that Bill will be badly scarred and perhaps have some wolfish characteristics. Bills parents and Fleur show up, and Fleur is insistent about staying with him, despite any danger or change to Bills appearance. This leads to revealing that the reason Tonks was upset was that she was in love with Lupin but he was reluctant because he was a werewolf.
Later, Hermione finds from research why Snape called himself the Half-Blood prince. Snape's parents were Eileen Prince (a pure-blood) and Tobias Snape (a muggle) so Half-Blood is correct, but Prince is his mother's surname. The potions book previously belonged to his mother.
There is an elaborate funeral for Dumbledore, who is buried in a white tomb on the grounds, but it is unclear whether Hogwarts will be reopened. Harry proclaims to the Minister of Magic, Rufus Scrimgeour, that Dumbledore is never gone as long as people at Hogwarts are still loyal to him. It appears that Ron and Hermione get together, but Harry basically breaks it off with Ginny because he says Voldemort would use people he loved against him. Harry plans to return to the Dursley's (due to the protection it would give him) but says that even if the school re-opens he will not come back, because he has to track down the rest of Horcruxes so that Voldemort can be killed.