Lydia Davis’s short-story collections tend to exceed the boundaries of a single book and become libraries. As you move among the pages, there is an effect of sampling the distinct contributions of quite a few writers. This could be connected with her skill as a translator of French literature — there are 13 rewritten fragments from the letters of Flaubert to be found in Can’t and Won’t — but that only accounts for one of the variant styles. Whatever its source, Davis’s range is all the more impressive for reading as a series of natural progressions.

Many of the characters we hear from in Can’t and Won’t, her first collection since winning the Man Booker international prize, are highly detail-oriented, and there is a variety of ways in which this affects their observations and interactions. Some walk high wires of introversion — take the protagonist of ‘A Small Story about a Small Box of Chocolates’, for instance, who offers the chocolates to a class of university students she teaches. Having fretted for weeks over the best way to enjoy a box of beautifully packaged Viennese chocolates (ought they to be shared, or ought she to keep them to herself, for some special occasion? But what kind of occasion: small triumph, large defeat? If they’re to be shared, which friends should they be shared with?), she immediately doubts that she has made the right decision.

“She told her students how it amazed her to think that a box of chocolates so small could be shared with 31 friends. She thought they would laugh, but they did not.” Everyone around her is finding this social interaction as ambiguous as she is, and her students formulate their own private permissions to relieve the strain: one asking if they are allowed to eat the chocolates, another asking to have a look at the ornate lid of the chocolate box. The narrator of ‘The Letter to the Foundation’ is similarly bound by her own painstaking process of deliberation following the receipt of a generous grant: “I have been attempting for many years to write the letter to you that I made the mistake of promising you ...”

Other stories provide tongue-in-cheek commentary on the extent to which we find ourselves enmeshed with the mathematics and minutiae of everyday life. In ‘Letter to a Peppermint Candy Company’, a consumer wishes to register mild indignation at the discrepancy between the stated weight of a tin of sweets and its actual calculated cost per pound. And the writer of ‘Letter to the President of the American Biographical Institute’ is keen to advise said president that she is on to the thinking behind the postal scam his company is pulling — it is almost certain that he has got hold of a list of “women who have accomplished something, because a woman who had accomplished nothing at all would surely not believe that her accomplishments deserved a ‘Woman of the Year’ award”.

A similar vein of comic angst runs through another story, ‘Handel’, in which a woman considers requesting some outside help to manage slippage between the serious and the superficial: “I have a problem with my marriage, which is that I simply do not like George Frederic Handel as much as my husband does. It is a real barrier between us.”

Elsewhere in the book, a report on the activities of a field of cows is full of the same kind of simple victory celebrated among human beings; that of getting through the day. “The third cow could not be bred because she would not get into the van to be taken to the bull. Then, after a few months, they wanted her to be slaughtered. But she would not get into the van to be taken to the slaughter. So she is still there.”

‘Their Poor Dog’ is a crisp, brief account of an unwanted pet that lays the dog’s hapless misery bare: “It had no good qualities. It did not know that.” Counterweights for this cutting clarity are found among the “dream pieces” interspersed throughout the book: short stories composed of a mix of the author’s own dreams and waking experiences and those related to her by family and friends. In some of these dream pieces we glimpse the dissolution of certain anxieties that attend us - about being correct, being well informed and well adjusted.

Reading ‘The Sentence and the Young Man’ places you in the middle of a group of people standing in the shadows, eyeing an ungrammatical sentence — “Who sing?!” — as it rests in an open dustbin. A young man has taken notice of the sentence and keeps walking past the bin, staring; as onlookers it is unclear to us whether the young man is taken with the sentence itself or slowly being wound up by the error in it. What to do? The spokesperson for the group makes a decision: “We will stay where we are, for fear that, at any moment, he will reach in quickly and fix it.”

Come to this one-book library for the mercurial gifts of its author; stay because the stories continually renew their invitation to be read inventively.

—By arrangement with the Guardian