The Subtle Knife really expanded the universe (universes?) of the series. As it says in the introduction, the first book was set in a world like our own, but different. This second book actually begins in our world, but then broadens in scope to a multiverse of settings that all seem to be connected, somehow or another. Characters can slip from world to world via tears--cuts?--in the fabric of the universes themselves.
On the flip side, while the ideas were interesting, I just couldn't get into the story or the characters. Lyra Silvertongue, the indomitable lead character from the first story, seemed relegated into supporting, and at times even...subservient?!...role in The Subtle Knife. She took a back seat to Will, a strong-headed boy with a tough past and fractured family. It's not that I didn't like Will, but I never really connected with him or understood what made him tick. The story in this book becomes much darker, and old villains from the first book resurface more powerful than ever, to a degree that seemed contrived.
Ultimately, the book ended on such a down note that my daughter and I felt compelled to take a break from the series and seek out lighter fare. It was disappointing, because we thoroughly enjoyed the strong female lead and empowering tale of the first book, and had hoped for more.