The movie script is very faithful to Larsson's novel, which I had read and enjoyed very much. Georgie hadn't read the book, but enjoyed the movie also, although found the violent scenes a bit off-putting. (They were more intense than I had anticipated--.)
The plot deals with a well-regarded investigative journalist, Mikael Blomkvist (Michael Nyqvist) who is facing the ruin of his career and a jail sentence after having been mislead into libeling a wealthy businessman. A different industrialist, Henrik Vanger (Sven-Bertil Taube) hires the now-available Blomkvist to dig into the forty-year old mystery of his niece's disappearance. While digging up the family skeletons, Blomkvist acquires the assistance of ace hacker Lisbeth Slander (Noomi Rapace), the "girl" of the title.
Both the protagonists have "issues": Blomkvist is dealing with depression and loss of self confidence, but he's a sunny day compared with Salander, who is an edgy and explosive bundle of hostility, aggression, and paranoia. She has a past involving criminal/mental health problems, most of which remain a mystery to all concerned. (Lisbeth's life is explained more in the sequel, US title "The Girl Who Played With Fire.") Between the two of them, they manage to solve the mystery of the disappearing girl, while, of course, stirring up more and nastier things than either had expected to encounter.
Rapace dominates every scene she is in, just as her character tends to steal the story from the rather low-keyed Blomkvist. (In the novel, we see more of Blomkvist's backstory, which makes him a more engaging character. That he isn't as charming in the movie is one of the frequent criticisms of the film, but I did not think it made a huge amount of difference.) The character of Lisbeth is in many ways as involvingly scary and psycho as Heath Ledger's "Joker" but fortunately Rapace, who has now made all three movies in Sweden, has survived the experience, which she has been quoted as saying she would not repeat for the US remakes being considered.
The movie is very faithful to the novel plot, which has a number of surprising twists to the main mystery, and is very well done in that regard. Settings, varying between urban Stockholm and the Vangers' rural retreat, are interesting and effective. The supporting cast is excellent.
All in all, a very well done, if harrowing movie. If you have read the novel and enjoyed it, odds are, you will enjoy this film version. If you haven't read the novel, it is still a very good mystery/suspense movie-just be warned that it is an uncompromisingly harsh and violent story.