The book I bought had this cover (above picture)
The other covers I saw in the bookstore:
The one I saw in Singapore:
That's Noomi Rapace in the cover.
I did not watch the movie yet. I say yet because I'm planning to if I could get my hands on the disc.
This time round Lisbeth Salander's guardian (a terrible one he is from the first book!), Advokat Bjurman, tries to get her into trouble. I wouldn't want to reveal much but Lisbeth got the upper hand near the end of the first book.
In other words, Advokat Bjurman would want her disposed off because she could destroy his career.
The second book focuses more about Lisbeth's past and the corrupt government.
Advokat Bjurman, as stupid as he is, actually got himself in trouble and the men he dealt with wants Lisbeth dead too!
Some of Lisbeth's colleagues (former) do not like her so they spread rumours about her, giving her a bad name (like murderer, satanist cult member etc)
Since it was all over the media and none of the rumours were true, Mikael Blomkvist uses his magazine company to fight back.
Of course there are fighting scenes between Lisbeth and burly guys.
If you guys are still confused (and I know you guys are), here's what Wikipedia had to say!
Mikael Blomkvist, publisher of Millennium magazine, has made his living exposing the crooked and corrupt practices of establishment Swedish figures. So when a young journalist named Dag Svensson approaches him with a meticulously researched thesis about sex trafficking in Sweden and those in high office who abuse underage girls, Blomkvist immediately throws himself into the investigation.
Blomkvist plans to run the story in an upcoming issue of Millennium. But shortly before the printing of the story, Dag Svensson and his partner are found shot to death in their apartment. Lisbeth Salander quickly becomes the primary murder suspect, as the police discover incriminating evidence against her at the scene of the crime. The next day, Salander's guardian, Nils Bjurman, is also found dead in his bedroom, shot with the same weapon.
Blomkvist tries to clear her name, although he can’t find her anywhere. When he does eventually make contact, it is to discover that Salander is more embroiled in his investigation than he could have thought possible. It turns out that for Salander, the trail of guilt leads close to home.