Frans Balder, a brilliant Swedish computer scientist, created a revolutionary artificial intelligence (AI) program when he worked at the Solifon company in the United States. He then suddenly quit his job, took his program, and returned to Sweden. Balder proceeded to remove his autistic 8-year-old son August from the abusive home of his ex-wife and her boyfriend and holed up at home with the boy. It seems that Balder had discovered a conspiracy involving Solifon, the National Security Agency (NSA), and Russian mobsters - and now feared for his life and his program.
Meanwhile, Mikael Blomkvist - famous investigative journalist for the magazine Millenium - is having problems. The magazine has been bought by a conglomerate that wants to remove Mikael from the editorial board and 'lighten' the magazine's features. Mikael could use a juicy story to buck up his career. This seems to be on the horizon when Frans Balder contacts Mikael to tell him he has a big, important story to tell.
Before Balder can meet with Blomkvist the computer scientist is murdered in front of his son August, who can't speak and doesn't seem to connect with what's going on around him. It turns out, though, that August is an artistic savant who might be able to draw a picture of the murderer. This makes him a target for the bad guys who, of course, don't want to be identified.
While all this is going on Lisbeth Salander - computer hacker extraordinaire - has been infiltrating computers around the world, including those of the NSA. Thus, she's discovered top secret information that's connected to the conspiracy Balder uncovered. Some of the NSA files, though, are super-encrypted and Lisbeth can't figure out the mathematical keys needed to open them.
As the story unfolds, Lisbeth rescues August from an assassination attempt and - while hiding the child - learns that he's also a math savant. Lisbeth uses the boy's math skills to try to crack the super-encrypted NSA files she's uncovered.
The basic premise of the story is that criminals are hunting August while Blomkvist tries to uncover the conspiracy Balder was going to reveal. Meanwhile, Lisbeth does her thing. She protects August, beats up men who abuse children and women, and infuriates people whose computers she's hacked. Lisbeth also must (once again) deal with a demented family member - this time her murderous fraternal twin sister Camilla. (Readers familiar with the trilogy know that Lisbeth is cursed with one of the worst families in the world.)
I'm a big fan of the Millenium Trilogy and was looking forward to this addition to the series. Sadly, in my opinion this book isn't as good as the previous ones. My main problems with the book:
There are intimations in the story that Frans Balder's AI program could potentially allow computers to take over the world and dispense with humans. I thought this thread might be important to the story but it went essentially nowhere.
To 'round out' the Camilla character the author resorts to a long expository chapter. In this section Hoger Palmgren (Lisbeth's former guardian) tells Mikael about Camilla - her history and relationship with her family - in great detail. This is an indelicate and tedious technique to familiarize the reader with a character. In addition, Camilla seems more like a comic book woman than a real person. She's so over-the-top gorgeous and manipulative that everyone seems to lose their senses around her. Because of this, the behavior of other characters around Camilla is simply not believable.
The conspiracy at the center of the story is too twisty and confusing. It's not until the very end of the book that I more or less understood what it was about - and then it didn't make much sense and I didn't believe it.
Though I wasn't satisfied with the story, I admire David Lagercrantz for taking on a difficult task. It's hard to add books to a popular series after the death of the original author. If Lagercrantz writes another Millenium book I'd probably read it to see if he's able to get the correct 'vibe'.
All in all, I'd recommend this book to fans of the series, but warn them to temper their expectations.