Before he was famous, the essayist Michel Eyquem de Montaigne brushed shoulders with death on a bridle path, some time in 1569 or early 1570. He was 36 and he liked to ride to get away from his inherited and elected ­responsibilities: a chateau and estate in the ­Dordogne and a seat in the Bordeaux parliament (or high court). He was on a placid horse and expecting an easy ride when what felt like a shot from an arquebus (the firearm of the day) knocked him and his horse to the ground: "There lay the horse bowled over and stunned, and I ten or twelve paces beyond, dead, stretched on my back, my face all bruised and skinned, my sword, which I had had in my hand, more than ten paces away, my belt in pieces, having no more motion or feeling than a log." When he regained consciousness, and afterwards his memory of what had really happened, Montaigne learnt that it was not a shot, but one of his servants, a muscular man on a more powerful horse, who had mistakenly charged past and hit him.

Previously, Montaigne had often imagined death. His reading in classical philosophy  the Stoics, Epicureans and Sceptics  encouraged him to brood on mortality and he had endured the recent deaths of his best friend (the humanist writer La Boétie), his father, younger brother and first-born child. But the riding accident cured him of morbidity. He awoke from it confused and vomiting blood, but went on to reinvent himself. He resigned from his position in Bordeaux and resolved to devote himself to writing the essays that would bring him immortality. As Sarah Bakewell writes in her new biography: "Don't worry about death became his fundamental, most liberating answer to the question of how to live. It made it possible to do just that: live."

Bakewell's sprightly book aims to do three things for Montaigne. First, it gives the general reader the basic facts of his life, sometimes summarised in point form. Second, it introduces those who do not know his essays to his wide-ranging answers to the question: how to live? "Don't worry about death" might have been the most fundamental, but there was a plethora of others: pay attention; read a lot, forget most of what you read, and be slow-witted; survive love and loss; use little tricks; question everything and so on. Bakewell takes each of these answers as a chapter heading and uses them to group her reflections on Montaigne in roughly chronological order.

Third, she splices her ­biographical material and extracts from Montaigne's writing with stories of how he has been received over time. She draws on the responses of his first enthusiastic readers, "who praised his Stoic wisdom and his skill in collecting fine thoughts from the ancients", and also on Descartes, ­Pascal, the 17th-century libertines, Enlightenment philosophers, the Romantics, 19th-century moralists, Nietzsche, ­Virginia and Leonard Woolf, Stefan Zweig, and others.

It was Leonard Woolf who called Montaigne "the first completely modern man" and argued that his modernity consisted in his "intense awareness of and passionate interest in the individuality of himself and of all other human beings". Non-human, or animal, beings also registered in Montaigne's intense awareness, as Bakewell, following Woolf, emphasises. She quotes Leonard's reminiscence of a traumatic episode in his childhood which reading Montaigne reminded him of. He was asked to drown unwanted day-old puppies and with retrospect he remembered them fighting death in the bucket of water: "As I would fight death if I were drowning in the multitudinous seas. It was I felt and feel a horrible, an uncivilised thing to drown that 'I' in a bucket of water."

Virginia Woolf is equally an inspiration for Bakewell in her mission to make Montaigne accessible to a contemporary, non-specialist audience. Woolf, she writes, "had a beautiful vision of ­generation interlinked in this way: of how 'minds are threaded together  how any live mind is of the very same stuff as Plato's & Euripides it is this common mind that binds the whole world together and all the world is mind'." It is precisely this capacity for living on through readers' inner worlds over long periods of history that makes a book like Montaigne's Essays a true classic, Bakewell argues.

Montaigne died of quinsy on 13 September 1592. Since his riding accident, he had fathered another five daughters, but only one survived into adulthood. He had become famous in France and Europe following the first edition of his essays in 1580. He had been elected mayor of Bordeaux in 1581 and participated successfully in the fraught politics of his day, blighted by the wars of religion. He went on annotating and adding to his essays until the end of his life; afterwards, editorial disputes broke out over what he had intended the final version to be. They continue to this day.

Bakewell manages to glide gracefully across current editorial ranklings over his texts without taking sides. Central as the essays are to her own approach to his life, it is ultimately his life-loving ­vivacity that she succeeds in communicating to her readers: "What he left behind was all the better for being imperfect, ­ambiguous, inadequate and vulnerable to distortion. 'Oh Lord,' one might imagine Montaigne exclaiming, 'by all means let me be misunderstood.'"

Ruth Scurr is the author of Fatal Purity, published by Vintage.

According to this latest biography the idea of writing about oneself was "invented" by Michel de Montaigne. A 16th-century nobleman as the father of all bloggers, and his Essays as the mother of all blogs? Certainly Montaigne's idea of the "essay" (from essai, meaning "trial") is far closer to the rambling, highly personal, internet-spawned version than the type remembered from school, where to stray hors sujet is the quickest way to lose marks.

As Montaigne himself recognised, his idea was indeed a new one: "This is the only book in the world of its kind, and its plan is both wild and extravagant." And this is because his subject, albeit "vain and worthless", was himself. Famously, his cat had a vital part in this; its gaze prompted him to recognise the idiosyncracy of perspective, as seeing a hare did for Virginia Woolf four centuries later  one of the many illuminating parallels Sarah Bakewell makes in How to Live. But his originality is also rooted in a debate as old as philosophy itself: the struggle between thought and language (which comes first?), and their mutual interdependency. By relaxing on that issue, and letting it all roll, he allows the reader to watch him think.

Like recent books on Proust, Joyce and Austen, How to Live skilfully plucks a life-guide from the incessant flux of Montaigne's prose. The 20 answers to the title question are drawn from the Essays, and act as a prism for aspects of Montaigne's life and thought. His childhood was a mixture of "bizarre limits"  none of the household allowed to speak to the lad in anything but Latin  and "almost unlimited freedom". Immersed in the classical philosophers, he was obsessed with death. The trauma of losing his close friend La Boétie to plague, and a near-fatal riding accident, knocked him out of morbidity into a cheerful acceptance of life, even after he had lost all but one of his children.

Bakewell suggests that his legal work as an assessor of complex cases at the Bordeaux court of inquiry "developed his feeling for the multiplicity of perspectives on every human situation . . . that runs like an artery through the Essays". This is most obvious in "On Cannibals", where he describes his encounter with members of the Tupinamba people from Brazil, and questions European assumptions of superiority. Perhaps the earliest example of cultural relativism, it contains a germ of socialism, too: what the visitors found strangest about France was its inequality; they were astonished that the poverty-stricken half did not take the rich by the throat "or set fire to their houses".

From the moment of publication in his lifetime, successive generations have felt that Montaigne was speaking to them as a close friend. Bakewell suggests that this intense empathy derives partly from the free-style form of the prose as it follows the "thousand paths" of one man's "random" reasoning, and partly from the author's confessed inadequacy: "I am free to give myself up to doubt and uncertainty, and to my predominant quality which is ignorance." Life is never like the glossy brochure, but nevertheless it is all we have got. Relax.

We relish the tolerant humanism in which Stefan Zweig, fleeing from the Nazis, found consolation before his suicide. "We are not so full of evil as of inanity," Montaigne notes, "nor so wretched as we are base." In the remarkable "On Liars", he admits to having a terrible memory, forgetting what he's read the day before; he keeps changing his mind about liking radishes; and he informs us that his moustache keeps the scent of whatever touches it.

No revolution is without antecedents: Bakewell gives her hero a firm philosophical pedigree in the Stoics, Epicureans and Sceptics, and in their collective cultivation of prosoche, or "mindfulness", through ataraxia, or "equilibrium"  which means having control over your emotions. The aim is not Heaven, but happiness in this world, or eudaimonia  "human flourishing".

How to Live also places Montaigne historically  and Montaigne believed the study of history was essential to self-knowledge. His was a period of soured ideals, when high Renaissance hopes, in Bakewell's words, "dissolved into violence, cruelty and extremist theology". Montaigne's famous tower was not of ivory: as the mayor of Bordeaux for four years, he was caught between violently warring factions, with fanatics on both sides; for a man not enamoured of religion (dismayed by its condoning of homicide and massacre), he did a remarkably good job. He fared less well in the following century: his book, banned in France by a zealous church for whom doubt was now devilish, became a primary inspiration for English writers as diverse as Laurence Sterne, Isaac Walton, Alexander Pope and William Hazlitt.

Bakewell insists that, despite its intense individualism, our newish century "has everything to gain from a Montaignean sense of life . . . and has been sorely in need of a Montaignean politics". His moderation, sociability and courtesy, suspension of judgment, his deploring of torture or killing in the name of lofty principles, and his observation in a world of corporate gloss that "the opposite of a truth has a hundred thousand shapes and a limitless field", still command our attention. How to Live is a superb, spirited introduction to the master, and should have its readers rushing straight to the essays themselves.

Adam Thorpe's novels include Hodd (Jonathan Cape).