The book is in my TBR pile, but I'm not sorry about seeing the movie first. An actual whodunit movie is very rare, and a good one is rarer still.
The Girl is Lisbeth, a Swedish "professional hacker". She's got all kinds of troubles: she's on some sort of probation due to (initially unspecified) legal trouble; her new probation officer thinks she's easy prey for sexual predation; gangs attack her in the subway.
And they're not kidding about that tattoo, either.
Lisbeth is ostensibly finishing up an assignment investigating Mikael Blomkvist, a journalist who's also in trouble: he published a story on a misbehaving industrialist, only to find the evidence on which he relied was elaborately falsified. Found guilty of libel, he's looking forward to some jail time. But before that begins, he's summoned off to work for the wealthy Vanger family, as one of their scions has become concerned with the 40-year-old disappearance and (presumed) death of young Harriet Vanger. Mikael's painstaking long-odds investigation comes to Lisbeth's attention via her ongoing compromise of Mikael's laptop. They join forces to solve the crime, but find themselves contending with Swedish Nazis—I hate Swedish Nazis—even more sexual perversion, general Swedish gloomy darkness, and Lisbeth's chain-smoking.
Be warned, it's not for the kids.