What a piece of work was James Boswell.

His father, Lord Auchinleck, didn't rate him, objecting to his incessant journal writing in particular. His mother was prone to mollycoddling and strict Calvinistic doctrine in equal measure. The son they raised was a welter of contradictions: vain and self-doubting; retenu and debauched; high spirited and prone to debilitating melancholy; physically courageous and terrified of ghosts. This, of course, is why he is so fascinating.

It is also why there is a frisson of doubt when Robert Zaretsky announces the plan for his book: "I have chosen to trace one particular aspect to the Scots life: his struggle with the great questions dealing with the sense and ends of life brought into being by the Enlightenment." Boswell was not always at his entertaining best when he struggled with the big issues. In fact, the giant thinkers into whose lives he was invited, or insinuated himself, sometimes lost patience with his eternal nattering on the eternal questions.

Samuel Johnson, whose biographer Boswell became, cut him off on freewill and predestination with "Sir we know our will is free and there's an end on't." Voltaire also ran out of patience when pressed by Boswell on the subject of the soul. "I know nothing of it," wrote the great Frenchman to the irritating Scot, "not whether it is, nor what it is, nor what it shall be."

However, any worries about Zaretsky drying out Boswell are assuaged by a colourful prologue when the author follows young James and his friend William Temple down Edinburgh's High Street. The invisible companion is a device favoured by American academics when describing 18th-century Edinburgh and Zaretsky uses it to fall in step with the two young men and point to the tumult that was Scotland's capital: sellers and sewage, cathedral and tenements, Kirk and brothels.

Boswell and Temple are on their way to ascend Arthur's Seat where, on reaching the summit, they yell "Voltaire, Rousseau, immortal names!" Boswell is clearly in a state of high excitement but this is only one of several examples of his use of spontaneous declamation. On approaching London for the first time, for instance, he surprised his fellow travellers by loudly expressing his pleasure when the stagecoach ascended the Highgate rise. In Utrecht, however, he "went out to the streets and even in public could not refrain from groaning and weeping bitterly". Even when crying out, Boswell dealt in extremes.

Boswell, of course, was destined to meet not just Voltaire and Johnson but Rousseau, Hume, Wilkes, the Corsican freedom-fighter Paoli and others. Whenever possible he made copious notes on their appearance, foibles and conversations. It was Johnson who inspired him to self-improvement through journalising (his father was an improver of a different order who, when Boswell was in Utrecht, wanted "to be informed of the method by which they [the Dutch] keep their cows so clean"). Johnson also instructed his young friend on the task of the biographer which, he believed, is to lead the reader's mind "into domestic privacies and minute details of daily life". It was advice that Boswell put to good use even before he employed it on his mentor.

Zaretsky is a fine writer, but it is his incorrigible subject that ensures a constantly entertaining read. Boswell is never still, either mentally or physically, and carries the author along on a tide of spirit and flesh. After reading fellow Scot Thomas Reid "On the Principles of Common Sense" and declaring it "a treasure", for instance, Boswell seduces a young woman in Berlin. On discovering that she was both married and pregnant he declares "Oho! A safe piece."

The philosophical traveller beards Rousseau and Voltaire at their retreats in Motiers and Ferney respectively, despite the two men being surrounded by other admirers and in the early stages of a prolonged enmity. The secret of Boswell's remarkable access to great men is difficult to pin down. His explanation was that "I have the art to be easy and chatty" but there is surely more to it than that. He declared on several occasions that he was "no bigot" as far as religion was concerned (Boswell was drawn to Roman Catholicism much to his father's horror) and he was liberal in his approaches to men of contending ideas. This was a stark contrast to his mentor Johnson who hated the very idea of Wilkes and considered that Rousseau and Voltaire were indistinguishable in their iniquity.

The book ends before Boswell becomes Boswell, as in the author of the "greatest biography in the English language". One thing that he and Johnson had in common was the black dog of depression which, in turn, was fuelled by a mutual fear of death or "annihilation". Zaretsky leaves Boswell after the death of David Hume when he "drank himself nearly blind ... and took a prostitute to the top of Castle Hill". Boswell had previously visited the cancer-stricken Hume in the hope that he would renounce his scepticism in the face of death, but the philosopher confounded him with his good cheer.

Boswell himself would die at 54, reduced by the long-term effects of gonorrhoea and drinking. But by then this romantic, rational, sceptical believer had already ensured his own immortality. Not bad for someone that Horace Walpole once dismissed as "the quintessence of busybodies".