He was so famous that fan letters addressed to "Mark Twain, God knows where" and "Mark Twain. Somewhere (Try Satan)" found their way to him; the White House accommodatingly forwarded something addressed to "Mark Twain, c/o President Roosevelt". Like Charles Dickens, Twain achieved immense success with his first book, became his nation's most famous and best-loved author, and has remained a national treasure ever since – America's most archetypal writer, an instantly recognisable, white-haired, white-suited, folksy, cantankerous icon. Since his death on 21 April 1910, Twain's writings have reportedly inspired more commentary than those of any other American author and have been translated into at least 72 languages. Despite being dead for a century, Twain is not only as celebrated as ever, he is also, apparently, just as productive: the first volume of his unexpurgated three-volume autobiography has appeared for the first time this month, a hundred years after his death.

Like the premature news of his death, however, reports that his autobiography has been embargoed for a century in honour of the author's wishes are somewhat exaggerated. He did indeed decree that it should be withheld for 100 years after his death, but various heavily edited versions have appeared since then, controlled by Twain's surviving daughter, Clara, his first biographer, Albert Bigelow Paine, and subsequent editors, all of whom cut anything they deemed offensive or problematic, standardised Twain's idiosyncratic punctuation, and reordered the narrative to create precisely the conventional cradle-to-grave structure he explicitly rejected.

Twain would have been apoplectic at the presumption: one of the letters he included in his drafts, reprinted in the autobiography's first volume, is a rebuke to an editor who dared to alter the great man's diction in his essay on Joan of Arc. Twain responded with an outraged rant restoring each correction with an explanation of his original choice and demanding: "Have you no sense of shades of meaning, in words?"

If the mot juste was always a priority – "I suppose we all have our foibles. I like the exact word, and clarity of statement, and here and there a touch of good grammar for picturesqueness" – structure was always a problem for Twain. As readers have noted since its publication, the plot of Huckleberry Finn, for example, deteriorates markedly at the end; Ernest Hemingway dismissed the story's resolution as a "cheat". Despite having been thinking about an autobiography since at least 1876, it wasn't until 1906 that the writer almost as famous for his lectures as for his books – he has been called America's first stand-up comic – found a method he liked. He simply hired a stenographer to follow him around and record his stories, while he talked and talked. He had decided by then not to publish for a century, in order that he might speak freely, without considering reputation or others' feelings. "From the first, second, third and fourth editions all sound and sane expressions of opinion must be left out," he decreed. "There may be a market for that kind of wares a century from now. There is no hurry. Wait and see." The spirit of this wish was followed mostly by accident, because the unfinished and multifarious drafts he left when he died made it extremely difficult for scholars to reconstruct.

Twain's eventual solution to the problem of autobiographical structure was characteristic: he ignored it, deciding instead to "start it at no particular time of your life; wander at your free will all over your life; talk only about the thing which interests you for the moment; drop it the moment its interest threatens to pale," and move on to the next subject. This is exactly what he does, confident that his "combined Autobiography and Diary" would be "admired a good many centuries" as inventing a form "whereby the past and the present are constantly brought face to face". The result runs to 500,000 peripatetic words across 2,000 pages, the first 700 of which comprise the first volume.

Twain famously announces at the start of Huckleberry Finn that "persons attempting to find a motive in this narrative will be prosecuted; persons attempting to find a moral in it will be banished; persons attempting to find a plot in it will be shot." A similar – if less threatening – caveat could be offered to readers of the autobiography. Those in search of the story of Twain's life should turn to any of a dozen biographies, by a roll-call of eminent American critics; those in search of explosive secrets should read the more controversial revisionist histories. Twain was by no means free of Victorian inhibitions, and he was vain; consequently there is much he would never reveal. Instead of cupboards and skeletons, the unexpurgated autobiography offers the "storm of thoughts that is forever blowing through one's head"; not the "facts and happenings" of Twain's life, but his voice. Fortunately for us, perhaps more than any other writer Twain was his voice; the result, for all its frustrations, is a revelation.

Born Samuel Langhorne Clemens in 1835, Twain spent his childhood in the backwater of Hannibal, Missouri in the decades before the US civil war. After apprenticing as a printer, he worked briefly as a journalist before training as a steamboat pilot, a career interrupted by the outbreak of war in 1861. He served fleetingly as a Confederate soldier before deserting ("his career as a soldier was brief and inglorious," said the New York Times obituary; in the autobiography Twain includes a sympathetic account of deserting soldiers being shot, without revealing the reason for his sense of identification). As would Huck Finn, the young Clemens "lit out for the territory" of the west, where Confederate forces were unlikely to pursue him, and sought his fortune in silver-mining. When that failed he returned to reporting, and adopted his pseudonym, a name derived from the call for safe water from riverboat pilots.

His journalism began to establish his reputation; he started lecturing and published his first book, The Celebrated Jumping Frog of Calaveras County, and Other Sketches in 1867. Two years later, The Innocents Abroad, the story of Twain's trip with a group of other Americans through Europe and the Holy Land (its subtitle was The New Pilgrims' Progress) was a bestseller, selling 100,000 copies within two years. He followed it in 1872 with Roughing It, another successful travelogue, and for the next 20 years, Twain produced instant classics, including not only The Adventures of Huckleberry Finn, but perennial favorites such as The Adventures of Tom Sawyer, A Connecticut Yankee in King Arthur's Court and The Prince and the Pauper, works of social criticism such as The Gilded Age and Following the Equator (an early indictment of imperialist racism that deserves rediscovery), Life on the Mississippi, blending autobiography and social history, and The Tragedy of Pudd'nhead Wilson, a novel using the device of babies switched at birth to expose the malignant senselessness of American racism.

Across their disparate subjects and audiences, what unites Twain's works is his quintessential Americanness. In Twain's obituary, the San Francisco Examiner wrote that he was "curiously and intimately American . . . He was our very own". Twain went further. Living in Europe in the 1890s, he wrote in his notebook: "Are you an American? No, I am not an American. I am the American." He was arrogant, but he wasn't wrong. It isn't just that Twain's books remain as popular as they are critically esteemed, or that his themes – the individual and society, free-market capitalism and social justice, populism and snobbery, deception and honour, idealism and cynicism, freedom and slavery, wilderness and civilisation – represent such characteristically American preoccupations. Twain was just as American in life, in his self-promotion, commercial ambition, pursuit of celebrity and narcissism. (As a child, Twain's daughter Susy began a biography of her famous father, in which she reports his explanation for never attending church: "He couldn't bear to hear any one talk but himself, but [. . .] could listen to himself talk for hours without getting tired, of course he said this in joke, but I've no dought [sic] it was founded on truth.") Equally American was Twain's mix of idealism and cynicism, sentimentality and scepticism. Hemingway pronounced in the 1930s that "All modern American literature comes from one book by Mark Twain called Huckleberry Finn"; but Twain didn't invent only modern American literature, he invented modern American authorship, as well.

And now it turns out he also felt he'd reinvented modern autobiography – a favourite American genre, given its emphasis on hubristic individualism and self-invention – calling his new method, with characteristic modesty: "One of the most memorable literary inventions of the ages . . . it ranks with the steam engine, the printing press & the electric telegraph. I'm the only person who has ever found the right way to build an autobiography." The comparison is revealing: like the old Scottish "makar" for poet, Twain saw his writing as an object he built; by no coincidence, he was in the forefront of debates about intellectual property. More than businessman, inventor, showman or even writer, at heart Mark Twain was a speculator. His instinctive grasp of branding and publicity was far ahead of his time, as he flung himself enthusiastically into 19th-century new media. Today he'd be blogging and tweeting his heart out – as long as he could monetise it. He sat for hundreds of daguerrotypes and photographs, displaying what he himself called a "talent for posturing" that suited the burgeoning cult of celebrity. Even his iconic white suit developed from commercial objectives: he first wore it to appear before Congress, arguing that copyright, which he viewed as a patent, should be extended in perpetuity. When that failed, he incorporated his pen name to establish it as a trademark, prompting the New York Times front-page headline: "Mark Twain Turns Into A Corporation". He designed his own board game, as well as "Mark Twain's Patent Self-Pasting Scrapbook", which sounds like something the Duke and Dauphin in Huckleberry Finn might sell. It is no accident that so many of Twain's characters are hucksters and hustlers, or that deception and opportunism are abiding themes in his writing.

He was susceptible to get-rich-quick schemes: the ventures he invested in and promoted – even as he was writing his greatest books – included vineyards, a steam generator, a steam pulley, a watch company, an insurance company, marine telegraphy, a food supplement called Plasmon, a chalk engraving process called Kaolatype, self-adjusting suspenders and the Paige typesetting machine, which bankrupted him at the height of his fame and forced him back on to the lecture circuit to pay his debts, in part, it's been suggested, to protect the value of his "honourable" brand. (In fact, James Paige, the absurdly impractical and possibly fraudulent inventor of the machine, inspires the most uncensored moment in the first volume. Previous editions included Twain's bitter remark: "Paige and I always met on effusively affectionate terms, & yet he knows perfectly well that if I had him in a steel trap I would shut out all human succour & watch that trap until he died." It turns out that Twain was more specific: "he knows perfectly well that if I had his nuts in a steel-trap I would shut out all human succour and watch that trap till he died.")

Twain understood publicity so well that he was merely amused when Huck Finn was banned by libraries across the US; when it was banned in Omaha, Nebraska, for example, he sent a telegram to the local newspaper, observing facetiously: "I am tearfully afraid this noise is doing much harm. It has started a number of hitherto spotless people to reading Huck Finn [. . .] The publishers are glad, but it makes me want to borrow a handkerchief and cry." Twain's cult of personality – as lecturer and novelist, commentator and social critic, travel and humour writer, gadfly and avuncular curmudgeon – was carefully judged, his folksy humour natural, but strategically deployed. He wrote out of a tradition of tall tales; this is why he was particularly suited to travel writing, which allowed him to be anecdotal and digressive, without much regard to structure or plot. Huck Finn itself is travel writing, in which the raft-trip down the Mississippi provides the picaresque structure for an episodic tale, an Edenic journey away from civilisation, as well as an occasionally frightening glimpse of the (all-too-human) wilderness.

And it is the anecdotal conversationalist who, for better or worse, dominates the unexpurgated autobiography. After a scrupulous introduction from the editors, explaining Twain's methods, problems and many false starts, the first volume opens with all those false starts. There is a long article he wrote as a young reporter about a shipwreck, reprinted verbatim; extended sections on Ulysses S Grant, which read more like a projected Grant biography than a Twain autobiography; pages minutely describing the Villa di Quarto in Florence, and so on. After 200 pages of throat-clearing (most of which will probably interest only specialists) comes another title page: "Autobiography of Mark Twain." And we're off, at last, sailing into the stream of Twain's consciousness.

Twain was always a barometric writer, with a knack for registering contemporary social pressures in sharp-eyed aphorisms that weren't merely quotable, but often well ahead of their time. His indictments of imperialism in Following the Equator, for example, read like post-colonialist mottos avant la lettre: "The very ink with which history is written is merely fluid prejudice"; "There are many humorous things in the world, among them the white man's notion that he is less savage than the other savages"; "Man is the only animal that blushes. Or needs to." The autobiography adds some new aperçus: "Man is the only [creature] that kills for fun; he is the only one that kills in malice, the only one that kills for revenge [. . .] He is the only creature that has a nasty mind." The autobiography is driven more often than not by outrage – personal outrage at times, as at the malfeasance of Paige, or the hapless "Joan of Arc" editor, or the American countess from whom the Clemens family rented the Florence villa, whom Twain roundly abuses. But most of the outrage here is social and political, including startlingly contemporary denunciations of American military interventions abroad, and condemnations of a society increasingly dominated by corrupt corporations, greedy capitalists, and vested interests. Writing of gilded age monopolists and robber barons, Twain's prescience is remarkable: he denounces Jay Gould, the financier and speculator, for example, as "the mightiest disaster which has ever befallen this country". He is equally critical of American foreign policy, condemning its imperialist ventures in Cuba and the Philippines and calling its soldiers "uniformed assassins". He discusses with some pride his affiliation with the "Mugwumps", a faction of Republicans who voted Democrat in the elections of 1884 in protest against the corruption of the Republican candidate. They were derided as traitors in an age when party loyalty was at a premium, but the Mugwumps were reform-minded independent voters. In this respect, they might be held to anticipate the Tea Party movement, but although Twain would have sympathised with the Tea Partiers' anti-tax, small government agenda, he would have loathed their historical ignorance and their susceptibility to manipulation by the same corrupt corporate interests he was railing against.

Twain's social impulses are not always angry; he was extremely gregarious and, if he was egotistical, he was also keenly interested in others, in ways that may frustrate readers in search of a self-portrait. There are far more sketches of others than of Twain, including many once-famous figures who have since been forgotten (such as the memorably named Petroleum Vesuvius Nasby). The better-remembered appear in tantalising glimpses: Harriet Beecher Stowe ("her mind had decayed, and she was a pathetic figure"), Lewis Carroll ("he was only interesting to look at, for he was the stillest and shyest full-grown man I have ever met except 'Uncle Remus' [Joel Chandler Harris]") and Helen Keller, with whom Twain became good friends; a letter from Keller ends this first volume.

There is a palpable sense that Twain is gathering momentum as the volume closes; the real treasures may be yet to come, and the next volumes apparently include a majority of the previously unpublished material. However tangential some of the early sections may be, there is also a great deal here to interest even the casual Twain reader. He does relate some (distant) family history, and tell some vivid stories of growing up in Hannibal. In 1849 Missouri was a frontier, where life was ugly, brutish and often short. Twain remembers witnessing much random violence, including stabbings and shootings, a slave brained with a rock "for some small offence", and two brothers trying repeatedly to kill their uncle with a revolver that wouldn't go off. There is a man shot through his eyeglasses, who shed tears and glass when he cried, and a local surgeon who stored his dead daughter in a cave (the model for "McDougal's cave" in Tom Sawyer) to see if the limestone would "petrify" her body – although this is an anecdote that requires the clarification offered by the "Explanatory Notes" at the volume's end. The exhaustive notes (250 pages of them) are often considerably more informative, factually speaking, than Twain: he never mentions, for example, that his father-in-law was an abolitionist who served as a "conductor" on the Underground Railroad, helped Frederick Douglass to escape and became his friend. Instead, Twain dwells – characteristically – on his father-in-law's success as a businessman.

All the memories are not brutal: there is an extended, evocative meditation, likely to become famous, describing childhood summers on an antebellum Southern farm, a memory of prelapsarian happiness eating green apples and watermelons; and a poignant tale of Jane Clemens teaching her son to consider a young slave boy's feelings. But most readers will doubtless be in search of the childhood tales of Tom Sawyer and Huck Finn – and Twain doesn't altogether disappoint, although he certainly digresses. He admits that Tom Sawyer was largely a young Sam Clemens, while Huck Finn was based on a real boy: "In Huckleberry Finn I have drawn Tom Blankenship exactly as he was. He was ignorant, unwashed, insufficiently fed, but he had as good a heart as ever any boy had . . . He was the only really independent person – boy or man – in the community, and by consequence he was tranquilly and continuously happy, and was envied by all of us . . . I heard, four years ago, that he was Justice of the Peace in a remote village in Montana, and was a good citizen and greatly respected." Again the helpful notes clarify: there's no evidence for this rumour; Blankenship was repeatedly arrested in Hannibal for stealing food, and died of cholera in 1889, soon after Huck Finn's publication.

It is largely thanks to Huck Finn's continued popularity, and controversy, that Twain has defied his own supposed definition of a classic as "a book which people praise and don't read". Most American schoolchildren still read Huck Finn, and if they don't, it is because it also remains the most frequently banned book in the US. Although it might seem paradoxical that a book could be both its nation's most frequently banned and its most beloved, this is not as silly as it sounds. Huck Finn is itself an ambivalent story about two of America's foundational preoccupations, individualism and race. Many readers cannot (or will not) distinguish between a book with racist characters and a racist book; the fact that the novel's sympathies are clearly with Huck and Jim, and against all the slave-owners (who are also all the white adults), is outweighed, for these readers, by its casual use of the word "nigger" – even though that was the only word that illiterate backwoods white boys in the 1840s would have used to describe a slave. Huck Finn and Tom Sawyer are rednecks, and Twain's language depends on verisimilitude for its comedy. Twain's appreciative ear for American vernacular is another reason for Huck Finn's abiding popularity; its vulgar, demotic language is why Hemingway celebrated it (and why Louisa May Alcott, for one, was among the first generation of readers to argue for banning it).

But most representatively American of all, perhaps, is the way Huck's struggle between selfish individualism and collective responsibility defines the book's action. Almost uniquely, Twain bridges the perpetual ideological divide that continues to cleave America today, right up to next week's midterm elections: he embraced the "mainstream media" of his day, and promoted democratic egalitarianism and social justice – but he was also a free-market libertarian whose small-town populism was marked by a fundamental suspicion of government. Huck Finn registers America's eternal ambivalence about individualism, simultaneously glorifying and condemning the doctrine that has so shaped the nation's history and continues to define it.

Those who finish Huck Finn still doubting Twain's own racial attitudes should read Following the Equator or Pudd'nhead Wilson, in which Twain excoriates the "one-drop rule" (the American law decreeing that "one drop of negro blood" made a person black): "To all intents and purposes Roxy was as white as anybody, but the one sixteenth of her which was black out-voted the other fifteen parts and made her a 'negro'." When writing in an educated voice, rather than Huck Finn's, Twain puts the then-respectful term "negro" in scare quotes, questioning the category itself. He also paid for the tuition of a young African American who wanted to attend Yale, saying that "he was doing it as his part of the reparation due from every white man to every black man". The autobiography includes some passing references to slavery and a revealing contemporary episode: Twain goes to a lecture supporting Booker T Washington's Tuskegee Institute and comments the next morning that although he'd met Washington many times before, he'd never realised that he was mixed race and had blue eyes: "How unobservant a dull person can be. Always, before, he was black, to me, and I had never noticed whether he had eyes at all, or not."

Similarly, if less frequently, Twain has been accused of misogyny, and it is true that his female characters tend toward the cardboard. But just as he learned over time to reject the casually cruel racism of his upbringing, so he was persuaded out of his early objections to women's suffrage by his wife, Olivia. A friend of feminists and suffragists, she persuaded him that women's innate moral superiority justified their presence in the public sphere. Soon Twain was donating money to suffragist movements and writing in his notebook: "No civilisation can be perfect until exact equality between man and woman is included."

Without question the greatest love that Twain reveals in this first volume (excepting perhaps self-love) is for his wife and daughters, especially his eldest daughter Susy, who died in 1896, at 24, of meningitis. Twain outlived his adored wife and three of his four children, which might put his supposed misanthropy and bitterness at the end of his life in perspective. In perhaps the autobiography's saddest moment, Twain tells himself that Susy's death was for the best, because life is unavoidably tragic: "Susy died at the right time, the fortunate time of life; the happy age – twenty-four years. At twenty-four, such a girl has seen the best of life – life as a happy dream. After that age the risks begin; responsibility comes, and with it the cares, the sorrows, and the inevitable tragedy. For her mother's sake I would have brought her back from the grave if I could, but I would not have done it for my own." The autobiography's many tender, grieving passages about Susy anticipate what Twain couldn't see coming: the death of another daughter, Jean, on Christmas Eve 1909. He spent his last months writing his account of Jean's death – "it is a relief to me to write it. It furnishes me an excuse for thinking" – which he declared should be the autobiography's final chapter. He died soon after.

At one point in this first volume, Twain observes that man is loving and loveable to his own, but "otherwise the buzzing, busy, trivial enemy of his race – who tarries his little day, does his little dirt, commends himself to God, and then goes out into the darkness, to return no more, and send no messages back – selfish even in death". But in this autobiography, Twain defies his own description and comes back to us, "speaking from the grave" just as he promised – and with 1,200 pages more to say.