PETER TAYLOR is the very least a principal contender for the peculiar distinction of being the most thoroughly undiscovered major writer in American literature. He turned sixty earlier this year, he has been publishing stories and other writings for four decades, he has been compared by critics of sound reputation with writers as notable as James and Chekhov - in fact, he is often referred to as "the American Chekhov" - yet it's a rare reader who has heard of him, such less read him. If a greater literary injustice has been done on these shores, it's escaped my attention.

The principal reason for this popular neglect doubtless is that Taylor has persisted in writing short stories long after the disappearance of those magazines that brought short fiction to the attention of a mass audience. Though his work appears from time to time in The New Yorker, he is entirely content to publish large amounts of it in journals of miniscule circulation; thus, for example, two of the stories in In the Miro District were published in The New Yorker, the other six in The Virginia Quarterly Review, The New Review, Shenandoah and The Sewanee Review.

The titles of all those "little" magazines may make Taylor sound like a writer of elitist fiction, but nothing could be farther from the truth. Unlike those short-story writers who dabbled in experimentalism and build up cult followings in campuses and garrets, Taylor writes stories that are entirely accessible to the general reader. The contemporary to whom he is perhaps most usefully compared is Eudora Welty - not because both are writers of incredibly graceful, witty and elegant fictions that disclose, beneath their surfaces of gentleness and gentility, a formidable toughness of mind.

Which brings us to In the Miro District , Taylor's first story collection in eight years (he published a book of short plays during that period) and his first book composed entirely of never before-collected stories since Happy Families Are All Alike , in 1959. It is an important book for that reason alone, but it may also prove to be important in enlarging Taylor's readership. It is the first of his books to be published by the firm of Alfred Knopf, a firm justly noted for its commitment to literary excellence and its willingness to advance the interests of writers whom it supports.

Taylor's small but ardently loyal band of faithful readers will at once recognize these eight stories for what they are: quintessential Taylor. There are, to be sure, some surprises; Taylor is a restless writer who delights in tinkering with new forms, and four of the stories are told him in a ruminative kind of narrative verse. But all of the stories share the fundemantal concerns that have dominated Taylor's career from the beginning.

They are, that is to say, thoroughly domestic stories. The family in its household is the central image in Taylor's work - the family revealing itself, slowly and sometimes astonishingly, in all its complexity, ambiguity, richness and mystery. The households are usually those of upper-middle-class families in Nashville or Memphis, but the dramas that take place within thim are universal; like Welty, Taylor is a regionalist only to the extent that he uses the territory he knows best as the bedrock upon which to rest work that ranges far afield in its larger subjects. Here, as always, he is exploring such endlessly provocative matters as the fragility of marriage - and, for that matter, all institutions designed to bind people together - the divisions between young and old, the sense of place, the ways in which people change and thus revel themselves, the perils of being trapped by circumsatnces.

The quintessential story in this small volume of quintessential Taylor is called "The Captain's Son." It is about a young man from Memphis of mony and social standing who comes to Nashville under clouded circumstances and proceeds, forthwith, to marry the lovely daughter of a prominent family of that city. They take up residence in her parents' house, in the "happy family" that recurs over and over again in Taylor's fiction. But eventually his presence becomes unbearable to his father-in-law, and an effort is made to find him a job that will get him out of the house. The effort fails disastrously. The young man browbeats his wife into joining him in alcoholism, and eventually they move away to Memphis. The story ends with this perfect passage of Taylor's prose: "Something happened to them that nobody but the very two of them could ever understand. And so they can't separate. They are too dependent on each other and on the good bourbon whiskey they drink together. Theirs is a sort of j oint boozing that sustains them in a way that solitary boozing or casual boozing with a stranger or even with some old friend can't do. They go on drinking together year after year. If their lives stand up under it, they may actually survive to a very old age. In fact, one imagines sometimes, waking in the middle of the night and thinking about them, that Tolliver and Lila just might have the bad luck to live forever - two of them, together in that expensive house they bought, perched among other houses just like it, out there on some godforsaken street in the flat and sun-baked and endlessly sprawling purlieus of Memphis."

It is scarely a novel theme, but Taylor embroiders it with a compassion and fullness of revealing detail matched by few other writers: nobody knows what is happening inside that most intimate of human arrangements, a marriage, except the two people in it - and often they don't even know themselves. Thus, in "The Throughway," the very model of a quiet modern marriage is shown to be riddled with contempt and hatred when unforeseen circumstances force the husband and wife to confront each other. "In "The Instruction of a Mistress," a venerable literary roue and his young lover disclose, in their private notes, the ways in which they are using each other beneath the guise of affection.

Over and again, the tangle of human connections and disconnections emerges as the main consideration of these stories. These men and women, young people and old, and caught in the web of circumstance. Taylor watches them struggle against entrapment and he observes the accomodations they make in order to achieve something approximating comfort; he describes what he sees without a scintilla of condescension, but rather with understanding and a certain wry resignation: this, after all, is simply the way it is.

At a time when so much of our fiction is self-consciously (and often self-servingly) "relevant," when writers chase after the headliness and the fads, Peter Taylor's fiction comes to us durable, rooted, solid. There is no flash and gliter here; this is quiet and honorable writing, content to seek the small truths that open the way to larger ones. Taylor may have no large audience now, but it is my unwavering conviction that in the year to come he will be read, admired and valued long after his more celebrated contemporaries have lost their claim upon our attention. Eventually we will come to understand that no one in our literature has mastered the myriad difficulties of the short story as completely as Taylor has, and that this mastery is greatness of a very real kind. The eight stories of In the Miro District should advance us immeasurably toward that understanding.