THIS FIRST MYSTERY, Laidlaw (Pantheon, $7.95), by Scottish poet-novelist William McIlvanney, who has won fiction awards back home, just may be the start of an absorbing new series. We have had the sagas of Martin Beck of Stockholm, Maigret of Paris, Gideon of London, and Van der Valk of Amsterdam. And now comes Jack Laidlaw of Glasgow, a dour, angry, compassionate, abrasive, moody Scottish police detective.

This Laidlaw is a complex and irritating man. A Scotsman overcast with Calvinistic guilt, he keeps Kierkegaard and Camus in his desk drawer and alcohol that he sips as a form of "low-proof hemlock" in a cache. He believes that the world would be a better place if people would have the courage of their doubts rather than their convictions. A man who inhabits paradoxes -- and incessantly broods over them.

McIlvanney's police-procedural story line is quite simple: An 18-year old girl has been sexually abused and murdered by a pathetic, troubled young man desperately trying to prove to himself that he is not a homosexual. Laidlaw tries to find the murderer before the girl's vigilante father and a calculating bookmaker who is afraid of what the boy may have learned in pillow talk from a gay discotheque operator.

What makes McIlvanney's first mystery special is the way that he writes and the way that he handles people and place. Glasgow, with its dreary back alleys and the hard, violent men of its pubs, is as much a protagonist as Laidlaw. McIlvanney, who lives and teaches in Glasgow, has smelled the city, listened to its sounds (be patient with the dialect for its flavor), and felt its presence. He writes sentences like this: "The ghosts of old smells drifted at them as they went, unexorcised by Lysol." Or: "His wasn't a face for forgetting. Angry, it belonged on a medieval church."

Laidlaw, who "Improvised every situation into a crisis," sometimes can be as exhausting to the reader as he is to Harkness, his young colleague, who provides a nice counterpart to his superior's overintrospection. So does Jan, Laidlaw's mistress, who cuts the brooding off with "Good night, Aristotle," observing: "You have to shut the door eventually on that stuff . . . and give yourself room just to be."

Sometimes McIlvanney doesn't shut the door soon enough on the brooding. And the novelist at time overreaches for an excessive, strained metaphor. But it is a small price to pay for a first mystery of such accomplishment and the promise of a superior new series. We certainly want more of Laidlaw, a policeman who doesn't believe in monsters any more than he believes in good fairies and can observe that people often choose guilts that they can handle as a way of hiding from the truth. There aren't too many cops like that in your standard police procedural.