The original 1958 edition of this novella was subtitled "A Requiem for the Detective Novel" -- a nugget of context unfortunately missing from this attractive new edition. This absent subtitle is rather important, because it very clearly identifies the taut little tale as one that challenges the traditional arc (crime, investigation, solution) of detective fiction. While the story does follow this arc, the "solution" subverts the qualities of reason, logic, heroism, and determination that are so often extolled in crime fiction -- and by doing so it acts as a critique of the modern era.
The plot is very simple, a little girl is found murdered in some woods on the outskirts of a small Swiss town. A master police detective on his last week of work before leaving on a plumb foreign contract takes the case, and, per the title, promises the mother of the slain girl that her daughter's killer will be brought to justice. A suspect is brought in and confesses, but the detective isn't satisfied, and pursues his pledge to the edge of madness.
The framework for the story is a little clunky, as it's related by the detective's former boss to an anonymous mystery writer. Some of the details also aren't crystal clear, for example, the murder is referred to as a "sex" crime, but it's also clearly established that there was no sexual element. However, these are minor points that should not obscure the power of the novella's grip, which, as others have pointed out, has echoes of Camus.
Note: The book has been adapted for film and television no less than six times! In reverse order, The Pledge (2001, USA) , Es Geschah am Hellichten Tag (1997, Germany), The Cold Light of Day (1996, UK/Netherlands) , Posledneye delo komissara Berlakha (1988, USSR) , La Promessa (1979, Italy) , Es Geschah am Hellichten Tag (1958, Germany).