This book is the sequel to The Girl with the Dragon Tattoo, which I really thought I already reviewed on here, but it sure doesn't look like it. My short review on facebook was: "A little slow to start, but very interesting and a good read. Can't wait to get my hands on the next one." Make sure you read that one first, and then get your hands on this one.
Stieg Larsson tends to set up his books with many different characters and storylines going on so that when you start you wonder where the heck he is going with all of it and how it will fit together, bit somehow it all works. The pacing in the beginning is slow, but it picks up as the book goes on. He has created some very interesting characters, particularly the main characters of Mikael Blomkvist, a journalistic crusader and ladies' man, and Lisbeth Salander, an astonishingly smart but socially inept hacker that has been declared incompetent by the state (she's "the girl" in both titles). This book brings more insight into Salander's psychological make-up as we learn more about the past, including who her father is. The main plot of the book centers around human trafficking and the sex trade in Sweden. Blomkvist is working with an author who intends to write an expose on the situation, but when he is murdered, and Salander becomes the main suspect, it is up to Blomkvist to discover what is really going on. Meanwhile, Salander stumbles upon a link to her past that she would very much like to sever, and though she doesn't want to rely on Blomkvist at all, she must accept his aid, at least a little.
The book definitely leaves you wanting more and sets things up nicely for the final volume in the trilogy, The Girl who Kicked the Hornet's Nest. Larsson has a very interesting and compelling style and it is extremely unfortunate that he is now deceased, so these 3 books are presumably the only ones we'll see from him. Highly recommended.