The canonised writers of the past have a tendency to assume a fixed expression in their readers' imaginations. Dostoevsky always appears in the same aura of morbidly enthralling hysteria; Proust in the same velvety atmosphere of hyper-attuned sensory receptiveness. To think of Tolstoy is to conjure, at once, the note of impassive grandeur, as of creation being set out in glittering ranks for inspection.

Anton Chekhov, whose short career was as momentous as any of these, has his own distinct tone and manner, but the impression it leaves is curiously elusive, offering reticence and hesitation in place of "personality", and a series of moods rather than a discernible attitude to life, even the attitude of uncertainty.

This elusiveness – a feature of both the life and the work – is a large part of what gives him his enduring fascination, as well as his striking modernity. In Chekhov literature seems to break its wand like Prospero, renouncing the magic of artifice, ceremony and idealisation, and facing us, for the first time, with a reflection of ourselves in our unadorned ordinariness as well as our unfathomable strangeness.

Ordinariness – the social fabric at its most drably functional – was to some extent his birthright. He was born in 1860, in Taganrog, a provincial town on the Sea of Azov. Said to be the shallowest sea on the planet, this minor appendage to the Black Sea shows up a muddy grey on satellite pictures, in contrast to the deep azure of the Black Sea itself. Whether this influenced the muted shading of Chekhov's prose – described by Nabokov as "a tint between the colour of an old fence and that of a low cloud" – history doesn't relate, but the city itself clearly became a key element in his imagination, forming the template for the stultifying provincial backdrops against which so many of his characters act out their dramas of ill-fated defiance or sullen resignation.

His grandfather was a serf who bought his family's freedom. His father, Paul, ran a grocery-cum-general store where Taganrog society congregated to purchase rice, coffee, paraffin, mousetraps, ammonia, penknives and vodka, and were duly cheated by the proprietor. Family lore records an occasion where a drowned rat was found in a cask of cooking oil. Instead of throwing out the oil, Paul had it "sanctified" by a priest, and continued selling it – an ur-Chekhovian episode, complete with a climax that is at once a non-event (business going on as usual), and a pitiless illumination of the father's character. A bullying, fanatically religious man as well as a total failure (he went bankrupt in 1876 and fled to Moscow with the rest of the family, leaving the 16-year-old Anton to fend for himself in Taganrog), the father too becomes a major generative element in his son's imagination. His presence can be felt in Chekhov's stories in the tyrannical father figures of "My Life" and "Three Years" as well as Jacob, the benighted zealot in "The Murder". In a more general sense, his spirit becomes absorbed into what might be called the negative pole in Chekhov's vision of reality: the force of oppression, petty-mindedness and outright cruelty that periodically discharges itself into the stories, sweeping over the characters as a sudden mood of melancholy or pure blackness (like the hallucinated Black Monk in the story of that title), or an impulse of vicious brutality, as in the notorious baby-killing episode of "In the Hollow".

As a human being – a doctor who went out of his way to help the poor and needy – Chekhov was unambiguously repelled by this aspect of life, and many of his better known remarks are either denunciations of it or defences of its opposite, which he identified chiefly as culture, rationality and scientific progress. There is the famous retort to Tolstoy, whom he revered as a novelist but rejected as a teacher: "Reason and justice tell me there's more love for humanity in electricity and steam than in chastity or vegetarianism," while the much-quoted lines from his letter to the poet Alexey Plescheyev are perhaps the clearest articulation of his "beliefs" such as they were: "My holy of holies is the human body, health, intelligence, talent, inspiration, love and absolute freedom – freedom from violence and falsehood, no matter how the last two manifest themselves."

But as an artist, Chekhov is more complicated than these apparently crystalline convictions suggest. Certainly his stories are full of people who espouse views very similar to the above – enlightened misfits, philanthropic gentry, civilised professionals (often doctors like himself) holding a candle for reason, justice and all the rest. But the stories themselves invariably subject this posture to challenges that cast doubt over its relevance, even its basic validity, so that to pin down an authorial point of view becomes impossible. Decency and rationality lead to failure, self-disgust and madness in pieces such as "A Dreary Story" or "Ward Number Six". In "The Princess", as in several other stories that feature do-gooding types, the philanthropic attitude is revealed as a rather nasty form of vanity. Even where it is sincere, it arouses baffling forces of resistance. Consider the well-intentioned couple in "New Villa", an engineer and his wife who settle in a rural spot after the engineer has built a bridge there. As if to extend the physical bridge into a social one, they attempt to befriend their peasant neighbours, only to find themselves opposed by malice and incomprehension at every turn. The bewildering irrationality of their treatment is brought home with gently comic poignancy by the story's ending, where the couple flee, selling their villa to a pompous government clerk who disdains the peasants, and is treated in return with paradoxical civility.

Comedy is of course another key element in Chekhov's imaginative armoury, and a further destabilising factor in the handling of his own "views". However tragic or despicable or exasperating the moralist in him found the world, the writer in him was constantly drawn to its comic variousness and oddity. No other writer has evoked boredom, dreariness, ennui with such richly entertaining specificity. Who but Chekhov could have conceived a story such as "A Hard Case", built around a living embodiment of stifling conventionality in the person of Belikov, who reduces a whole town to his own state of cowering joylessness before the inhabitants finally turn against him? The exorcising of such baleful spirits seems to have been one of the primal drives underlying the production of the 800-odd stories Chekhov left behind: happiness, in his work, almost always occurs against an encroaching darkness that requires constant warding off. In life he was known as an aficionado of jokes, pranks, festivities, the burlesque spirit in general. And his writing career, which he embarked on to make money for his family after his father's bankruptcy (as well as to pay for his own medical studies), began strictly as a comic enterprise: skits, spoofs, ­"humour pieces" full of daft names and slapstick come­uppances, churned out for sale to popular ­journals.

"Oh, with what trash I began," he ­remarked later in life, "my god with what trash." Turning away from "trash" seems to have entailed turning away, not from comedy itself, but from a certain conception of what constitutes a "story". The traditional idea, seen at its best in, say, Pushkin's "Queen of Spades", or Maupassant's much maligned "The Necklace", tend­ed to rely heavily on contrivance to achieve its effects – ghosts, coincidences, characters suddenly going mad, priceless jewels turning out to be fake, and so on. The aim was to create a high stakes drama in a short space and above all to bring off a surprise ending; the twist in the tail that reverses one's understanding of what has gone before.

While Chekhov never totally abandoned this approach, he discovered early on how to create compelling stories that mirrored – or seemed to mirror – the casual movement of reality itself. In "The Steppe", the first of his stories to be published in a serious literary journal, the artless artistry of his later masterpieces is already substantially evolved. Here, instead of neat twists or morally pointed drama, we have simply the flow of life registering itself on the senses and emotions of a nine-year-old boy as he journeys with his uncle across the Ukrainian steppe.

There are fluctuations of mood, ranging from lyrical delight at the natural beauty of the steppe, to brooding menace as the bully Dymov begins picking on the boy. But rather than pressing these fluctuations into service as steps towards some definitive conflict or revelation, Chekhov traces them purely for their own sake, as events in his protagonist's consciousness. Most writers, having sketched a character like Dymov in such deftly illuminating detail, and built up the hostility between him and the boy with such psychologically precise touches, would have found the temptation to stage a showdown between them irresistible, but Chekhov merely lets the pent energies of the situation disperse into an inconsequentiality that even today – after so many imitators have made the gesture commonplace – feels shockingly true to life.

Meanwhile the comic impulse, ousted from its early role in shaping the structure of the stories, becomes reabsorbed into the grain of the narrative itself, blending in with the other principal tonalities to form the ­characteristic hybrid Chekhovian note, where the tragic and the farcical, the lyrical and the prosaic, the tender and the grotesque are inextricable from each other.

Time and again moments of potential solemnity are deflated by some mundane detail, the effect of which is a kind of constant assertion of the lifelike over the "literary". Gurov, in "A Lady with a Dog", famously responds to Anne's sudden onset of remorse after they consummate their affair, not by attempting to rise to her anguished, high-flown rhetoric, but by cutting himself a slice of watermelon and eating it in silence. Gusev, in the story of that title, dies a death as ­moving, in its understated way, as any of the great deaths in short fiction, but its pathos is all implicit; the outward detail being noted in precisely the kind of droll, off-kilter manner in which Gusev himself sees things. In death, sewn into a canvas bag, he is described as resembling – of all things – "a carrot or radish – broad at the head and narrow at the base". And in a stunning, unexpected coda that at once makes light of his death and confers on it a curiously sublime apotheosis, the story follows his corpse after it is thrown overboard, noting the reactions of the "delighted" little pilot fish as it sinks past them, observing the shark that "nonchalantly" rips open the bag, and then veering into a passage in which the casual and the cosmic mingle with transcendent strangeness: "Overhead . . . clouds are massing . . . one like a triumphal arch, another like a lion, a third like a pair of scissors."

With its final image, of the sky ­taking on "tender, joyous, ardent hues for which human speech hardly has a name", Gusev brings us close to the essence of Chekhov; the underlying state of mind that produces the two basic moods of his work – wonder and ­horror.

Again and again, as emotional pressures mount in his characters, the crisis expresses itself in this state of bewildered disjuncture. Olga, the compulsively loving woman in "Angel", enters it as soon as she finds herself without a mate, describing it in her homely way: "You see an upright bottle, say – or rain, or a peasant in a cart. But what are they for: that bottle, that rain, that peasant? What sense do they make? That you couldn't say . . ." The more intellectual narrator of "My Life" puts it in terms of alienation from his fellow townsfolk: "What kept these sixty-five thousand people going? That's what I couldn't see . . . what our town was and what it did, I had no idea." Sometimes even the inner life becomes a source of mystery. Gusev again, as he learns that he is going to die, experiences a kind of climactic bafflement at his own feelings: "A vague urge disturbs him. He drinks water, but that isn't it. He stretches towards the port-hole and breathes in the hot, dank air, but that isn't it either. He tries to think of home and frost – and it still isn't right."

"You confuse two concepts," ­Chekhov wrote to his friend AS Suvorin, who had been pressing him to be more definitive in his statements as a writer, "the solution of a problem and its correct presentation. Only the second is incumbent on the artist." The remark is generally taken as a kind of miniature manifesto; a defense of his own highly original, open-ended narrative art. This is valid as far as it goes, but it would be a mistake to regard Chekhov as a purely technical or aesthetic innovator. The radical attentiveness to emotion, the embrace of the trivia and inconsequentiality of daily existence, the fading ellipses as one mood gives way to another, the unpredictable shapes of his stories (ask yourself, as you read them, where they might be going: it's almost always impossible to guess, and yet when you get there it feels inevitable and entirely natural), the endings that "solve" nothing in the conventional sense but do indeed finalise the "correct presentation" of the problem – all this is premised, not on some simple ambition to strike a new note, but on a new way of looking at reality that required new methods to express it. There had been sceptics, agnostics, doubters, questioners of every kind before Chekhov, but perhaps no writer in whom the utter mysteriousness of existence was felt so deeply, or counterpoised by such ­inexhaustible interest in the teeming variety of forms – human and otherwise – in which it manifests itself. To have found a way of expressing both, with such profligate inventiveness and such apparent ease, was, above all else, the mark of Chekhov's genius; his unsurpassed greatness as a teller of stories.

A new Folio Society edition of Chekhov's stories is published this month. www.foliosociety.com