Reykjavik Nights by Arnaldur Indriðason

The loner Erlendur has recently joined the police force as a young officer. The beat on the streets in Reykjavik is busy: traffic accidents, theft, domestic violence, contraband… And an unexplained death. When a tramp he met regularly on the night shift is found drowned in a ditch no one seems to care. But his fate haunts Erlendur and drags him inexorably into the strange and dark underworld of the city.