If you liked The Millenium Trilogy by Steig Larsson,
try these authors:

Books with tough females characters seeking justice:
Britt Montero Mysteries by Edna Buchanan.  First title is Contents Under Pressure.
Miami crime reporter Britt Montero will follow an investigation wherever it leads, and however dangerous it becomes.
Aud Torvingen series by Nicola Griffith.  First title is The Blue Place.
Aud Torvingen retires from the police force at 29 when she inherits a fortune.  She’s free to be completely ruthless in following her sense of right and wrong.  But can she find some way to connect to those who care about her, or is she as cold inside as the people she hunts?
Maureen O’Donnell novels by Denise Mina.  First title is Garnethill.
Maureen O’Donnell, abused as a child and unstable as an adult, finds herself the prime suspect in the murder of her married boyfriend.  With seemingly the whole world against her, she sets out to solve the crime herself.
Kathleen Mallory series by Carol O’Connell. First title is Mallory’s Oracle
Kathleen Mallory was a tough street wise kid when she was adopted by a police sergeant at the age of 10. Now a cop herself, she is both damaged and brilliant, and still playing by the rules of the street.

More tough female P.I.s:
*V.I. Warshawski series bySara Paretsky.  First title is Indemnity Only
Sharon McCone series byMarcia Muller. First title is Edwin of the Iron Shoes

Kate Martinelli series by Laurie R. King.  First title is A Grave Talent

Books with a Swedish setting

Sun and Shadow by Ake Edwardson
Erik Winter is the youngest chief inspector in Sweden: he wears sharp suits, cooks gourmet meals, has a penchant for jazz, and is about to become a father. But a bloody double murder on his doorstep signals the beginnings of trouble..

Blackwater by Kerstin Ekman
Annie Raft travels to Blackwater, a remote Swedish village, planning to join a commune, but stumbles on a brutal murder. Eighteen years later, the crime still unsolved, Annie recognizes the man she saw fleeing the murder scene.

The Princess of Burundi by Kjell Eriksson
When a jogger stumbles upon the mutilated body of the local reformed troublemaker, Inspector Ann Lindell takes time off from maternity leave to engage in a deadly game of cat-and-mouse with a vicious murderer.
Unspoken by Mari Jungstedt
Gotland Police Inspector Anders Knutas investigates the suspicious death of photographer Henry Dahlstrom, who just happens to have sexually explicit photos of another murder victim in his darkroom.
Sun Storm by Asa Larsson
Attorney Rebecka Martinsson returns to her hometown when a charismatic preacher is killed, and the victim’s sister, Rebecka’s childhood friend, is accused of the crime.
The Man from Beijing by Henning Mankell
In the aftermath of the 2006 massacre of nineteen people in a Swedish village, Judge Birgitta Roslin, a granddaughter of two of the victims, discovers the nineteenth-century diary of a gang leader that reveals the case's eerie connections to the abuse of Chinese slave workers. (See also the author’s Kurt Wallander series)
Mind’s Eye by Hakan Nesser
Janek Mitter woke one morning with a brutal hangover and discovered his wife of three months lying facedown in the bathtub, dead. With only the flimsiest excuse as his defense, he is found guilty of a drunken crime of passion and imprisoned in a mental institution. But Chief Inspector Van Veeteren’s suspicions about the identity of the killer are borne out when Mitter also becomes a murder victim.
Echoes from the Dead by Johan Theorin
Twenty years after Jens disappeared without a trace from the island of Oland, a package is mailed to the boy's grandfather that contains the worn and mended shoe of a child, prompting the grandfather to contact the child's mother, resume the hunt for the boy, and make a shocking connection between Jens's disappearance and the island's most notorious murder case.
Detective Inspector Huss by Helene Tursten
A local businessman’s suicide turns out to be murder, and Goteborg’s Violent Crimes Inspector Irene Huss finds her investigation leading to an underworld of drug dealers and biker gangs.