Spoilers ahead for the earlier ones.
Opens a bit differently. The first chapter is of the Prime Minister get posted with news from Fudge, concluding with the news that he's no longer Minister of Magic. As infodump, I don't think it works. And then we have a scene with Death Eaters, where Snape, Narcissa and Bellatrix discuss a task assigned to Draco by Voldemort, and Snape takes an Unbreakable Vow to help him.
Back to Harry. Dumbledore brings him to the Burrows, but first, brings him along to recruit a teacher for Hogwarts. (They are, after all, short a Defense Against Dark Arts teachers.) It's Harry who actually persuades him. And then to the Burrows, where the danger of Voldemort is much more real, though fortunately open, and many of the Weasleys do not approve of Fleur as Bill's fiancee. They also see that Draco is up to something when they go shopping.
Arriving at school, they find that Slughorn has actually been hired for Potions. This is because Snape is finally getting the position of Defense Against the Dark Arts professor. Meanwhile Dumbledore is giving Harry some additional lessons -- showing him memories of people who had seen Voldemort in the past, and piecing together what can be guessed.
The story involves Harry's suddenly becoming good at Potions[Spoiler (click to open)]which has surprisingly little plot impact for the space it takes up, accounts of people framed for murder, Draco's habit of disappearing, Tonks' hair turning mousy with apparent grief, the Minister of Magic trying to recruit Harry and the scars on his hand from Dolores Umbridge's quill, and much more.
Though I do note that at my first reading, I instantly thought of[Spoiler (click to open)]Regulus Black when the locket was opened. It's a bit disappointing that they do not remember they have heard of someone with initials R.B. who was murdered by Death Eaters, under circumstances when he would know it and perhaps want a revenge.