Police Procedural
This classification of crime fiction books covers a lot of ground, and the police procedural arguably is not a "real" genre. It covers a wide range of mystery types - from cosy to bloody noir, from gentle work-place banter to traumatic psychological thrillers, it's all here.
The crimes are usually investigated by one or more police detectives (with help from forensic experts, legal professionals, medical examiners, psychologists etc).
Some of the best-loved crime fiction authors wrote in this genre: PD James, Colin Dexter, Georges Simenon, Reginald Hill, and more recently Jo Nesbo and Ian Rankin.