When fans first catch up with her in “The Girl Who Kicked the Hornet’s Nest,” she’s in a hospital emergency room, fighting for her life: there are wounds in her shoulder and hip and a bullet lodged in her brain, and should she recover, she is supposed to stand trial for three murders. Her father and worst enemy, Alexander Zalachenko, is in the same hospital, with a damaged foot and an ax wound to his face. And her friend and former lover, the investigative reporter Mikael Blomkvist, is under arrest for possession of an illegal weapon.

“Hornet’s Nest” is the last novel in Larsson’s Millennium series that Larsson, the crusading Swedish journalist, completed before his sudden death from a heart attack at the age of 50 in 2004. It’s also a thoroughly gripping read that shows off the maturation of the author’s storytelling talents.

The trilogy’s first installment, “The Girl With the Dragon Tattoo,” depended solely on the irresistible odd-couple appeal of Salander and Blomkvist as a new age Nick and Nora; its plot devolved into a preposterous mashup of bad serial-killer movies. The second installment, “The Girl Who Played With Fire,” attested to the author’s improved plotting abilities, moving backward into the past even as it accelerated toward a vicious and violent conclusion. Now, in “Hornet’s Nest,” Larsson effortlessly constructs an immensely complicated story line that owes less to the “Silence of the Lambs” horror genre than to something byJohn le Carré. It draws together many (though not all) of the loose ends scattered throughout the trilogy, while twining them around a political conspiracy within Sweden’s Security Police (SAPO) — a conspiracy that not only jeopardizes Salander’s freedom but also threatens the country’s very Constitution.

Why have Larsson’s novels become such a global publishing phenomenon? What accounts for the first two volumes’ selling about 3.5 million copies in the United States? The blood-splattered story lines and the author’s enthusiastic manipulation of genre clichés, of course, have something to do with it, along with his untimely death (and unsubstantiated rumors that he might have been killed by extremist right-wing groups). The novels’ central appeal, however, remains Salander herself: a heroine who takes on a legal system and evil, cartoony villains with equal ferocity and resourcefulness; a damaged sprite of a girl who becomes a goth-attired avenging angel who can hack into any computer in the world and seemingly defeat any foe in hand-to-hand combat.

The narratives of all three books are ultimately explorations of Salander’s past, and it is this past that explains the mysteries of her personality. For that matter, the page-turning suspense of these books has less to do with the pyrotechnics of Larsson’s often contrived plots than with the reader’s eagerness to understand how Salander came to be the way she is — why she is so leery of emotional commitment, why she has a deadly score to settle with her dreaded father, why she values survival above all else.

With Blomkvist, Larsson has given Salander an appealing partner and foil — a romanticized version of the workaday investigative reporter; a smart, haimish Everyman who also happens to be a genuine chick magnet. Blomkvist, we’re told in one of the earlier volumes, believes that “the golden rule of journalism was that there were always people who were responsible. The bad guys.” And this conviction becomes a moral imperative that drives him to chase down the people who have victimized Salander, and to slash away at the tentacles of governmental, corporate and judicial corruption that he sees strangling the country. Indeed the Sweden in these books is not the shiny, clean utopia where everyone drives Volvos, shops at Ikea and listens to Abba, but a noirish place where the dark emotions of Bergman and Strindberg reign, along with a malign brand of politics and law.

Larsson had founded an antifascist magazine called Expo and was an expert on antidemocratic right-wing extremist organizations, and his journalistic chops lend an air of verisimilitude to Blomkvist’s investigations into SAPO and several parallel investigations, run by the government and a detective agency, into Salander, Blomkvist and the Security Police.

So how are SAPO and Salander connected? What could rogue members of the force possibly want with a punked-out young woman, and why are they hoping to use her coming trial to send her away for good?

Larsson’s premise is as convoluted as it is melodramatic. Salander’s thuglike father was apparently an important Soviet agent who defected and sought asylum in Sweden in 1976; he was so valuable and secret an intelligence source that a special section of SAPO evolved to protect him. When he fell into sleazy business deals or beat up women, zealous section members got into the habit of cleaning up after him. They regarded Salander, who had vowed revenge on her father for nearly killing her mother, as a huge security risk and used a corrupt psychiatrist to get the girl, then a 12-year-old, committed to a mental institution.