FOR the people in ''The Progress of Love,'' storytelling is a way of seeing and remembering, a mundane but necessary art. In the title story, the narrator recounts how her father watched her mother burn her unwanted inheritance in the kitchen stove; though probably untrue, the story serves as a testament to what she believes about them and the nature of love. Another woman tells a story about how she met her first husband while singing madrigals at college, a neat story of destiny between ''a skinny innocent bit of a lad with a pure sweet tenor'' and ''a stocky little brute of a girl with a big deep alto.'' And a third speaks of how she and her husband ''invented characters'' for their children, casting each daughter in a specific role.
In ''Monsieur les Deux Chapeaux,'' the telling and retelling of familiar stories serves a ritual purpose of alternately soothing and discomfitting various family members, and in ''Jesse and Meribeth'' a teen-age girl tries to impress her best friend by inventing an outrageous story about an affair with a married man - a story that ironically fulfills itself even as it's exposed as a lie.
As this volume and several earlier collections (most notably ''The Moons of Jupiter'' and ''The Beggar Maid'') attest, Alice Munro is herself a remarkable storyteller who, having slowly acquired a faithful audience outside her native Canada, now richly deserves recognition as one of the foremost contemporary practitioners of the short story. Though her tales occasionally display an overcrafted sense of irony (''Monsieur les Deux Chapeaux,'' which involves two possible attempts at murder, is one such example), the best possess a wonderfully organic coherence. They create complete fictional worlds for the reader, but their wholeness has the pleasing irregularity of something found in nature. Instead of squeezing the ambiguities of relationships and feelings into a neatly molded form, the stories accommodate them, taking on in the process the complicated texture of real life.
Families, the overlapping and intersecting lines of emotions connecting parents and children, husbands and wives, the ''dangerous mix-ups'' of domestic life - these are the subjects Ms. Munro returns to in these stories and she delineates them with an old-fashioned amplitude of emotion and language. She is concerned not only with the different configurations of love that occur in the wake of divorces, separations and deaths, but also with the ''progress'' of love, the ways in which it endures or changes through time: how the weight of intimacy can suffocate a marriage, as easily as loft it into new passion; how disappointments, an apprehension of loss, can be handed down generation to generation, mother to daughter, as easily as the capacity for caring; how history repeats itself, when the man who spurns one fiancee for another decides, years later, to leave the wife for another woman.
But while so many of the characters in these stories leave their lovers or their families, few ever exit completely. Instead, they seem to hover about the corners of their former lives, like ghosts who are reluctant to depart - new girlfriends are introduced, quite cruelly, to former wives; anniversaries are celebrated years after a spouse's defection.
Indeed, the characters in Ms. Munro's stories seem perpetually torn between freedom and domesticity, the need for independence and the need to belong. One man seems to trade in wives and girlfriends, regularly, as soon as their failure to live up to a designated role - of ''hippie,'' ''trollop,'' etc. - threatens him with real intimacy; another determines to leave town when his girlfriend hints she might be pregnant.
In ''White Dump,'' a woman relishes the idea of staying behind as her family goes off for an airplane ride, cherishing the prospect of ''emptiness, a lapse of attention,'' that will permit her to momentarily misplace her customary enthusiasm and watchfulness. And in ''Miles City, Montana,'' the narrator also yearns for ''a place to hide'' from the demands of running a household. She wants to ''get busy at my real work, which was a sort of wooing of distant parts of myself,'' only to realize in the wake of a swimming pool accident that her self-preoccupation has nearly resulted in her daughter's death.
But while death and overt violence occasionally do make their appearance in these stories, the characters tend to be haunted by a more abstract premonition that life is precarious and fragile, that things can shift, fade or disappear with the suddenness of a mood change. A man abruptly leaves his wife and daughter for a woman whose camper has broken down; a woman meets the man who will become her new lover during a celebration of her husband's 40th birthday. Even when everything seems smooth and scheduled and fine, ''the skin of the moment can break open.'' ''With all their happiness and hugging and kissing and stars and picnics,'' a woman can find her husband's side of the bed empty and leap to the conclusion that he's ''done away with himself.''
In the end, Ms. Munro suggests, one of the reasons for this sense of aloneness and peril is the utter subjectivity of truth, our inability to see things through others' eyes. In the title story, for instance, a woman contends that her late mother tried to hang herself out of a sense of despair; her sister maintains that she did it as a joke, in order to provoke their father. Which version is correct? Can the truth ever be ascertained?
Drawing upon her seemingly infinite reserves of sympathy, Ms. Munro writes, in these stories, from a multitude of perspectives - shifting points of view, from one character to another, as well as back and forth in time. The results are pictures of life, of relationships, of love, glimpsed from a succession of mirrors and frames - pictures that possess both the pain and immediacy of life and the clear, hard radiance of art.



THE PROGRESS OF LOVE 
By Alice Munro. 
309 pages. Alfred A. Knopf. $16.95.