The Golden Compass, I decided to reread recently when the girl I nanny for started reading it. She hasn't yet gotten to The Subtle Knife, but I have found that this trilogy is not an easy one to read any other way than straight through, so that's what I did.
The Subtle Knife is a much shorter book than either The Golden Compass or The Amber Spyglass. Like The Emperor Strikes Back, it's kind of an intermediary book, setting things up for the third and final installment. The story also gets continually darker throughout this book.
It starts out in our world, where we meet a boy named Will. He inadvertently finds his way into another world, where he meets Lyra. This isn't her world either, but it is a world that will play a huge part in the course of the story.
Lyra is on a quest to find out more about Dust, which she has been learning about using the alethiometer (the "golden compass"). The alethiometer guides her to a scientist in Will's world who is able to help her learn even more. At the same time, her enemies are closing in on her and Will, and during the course of trying to get away, they happen upon another important artifact: the subtle knife, which will also play a huge role in the course of the story.
As I said, the story become ever darker in this book, as does the church's (from Lyra's world) mission.