One hundred and thirty. That, give or take a ménage à trois, is Ian Kelly's estimate of the number of notches on the bedpost of Giacomo Casanova, the man long renowned as the world's greatest lover, whose name now lends itself with fitting promiscuity to both a stylish honeymoon hotel and a clinically diagnosed fondness for philandering. It's an impressive figure, especially for a man who began his career as a libertine by studying for the priesthood. He ended it, having found his true vocation, by writing the world's first great kiss-and-tell memoir, the 12-volume Histoire de ma vie

But there's more to Casanova than his reputation implies. He was a prolific author of fiction and philosophy, a connoisseur and cabbalist, a student of medicine and an accomplished musician. He was also, as Kelly reminds us, one of the 18th century's most prodigious travellers. Each chapter of this immensely enjoyable biography is headed with a neat illustration of a carriage, as it might be, or a gondola, the changing forms of transport bearing witness to Casanova's wanderings across Europe and the level of luxury matching the rise and fall of his material fortunes. While those fortunes rose and fell, the number of conquests kept rising. But how much of his extraordinary story can a biographer really believe?

The surprising answer, according to Kelly, is most of it. You could trust Casanova's word, even if you couldn't trust him with your daughter. That said, even contemporaries had their doubts. When he entered a Venetian seminary at the age of 18 to begin his theological studies, the young Casanova "felt slighted ... he was insulted by the need to sit an exam, insisting, correctly, that he was already a doctor". It was true. He had gained his legal qualifications at 18, shortly before losing his virginity.

Kelly writes with just the right blend of scholar and libertine, neither prudish nor prurient, and with an engagingly relaxed turn of phrase. I cringed for a moment at his description of Casanova's "adolescent snogging", then reflected that Casanova, the aged roué with the well-notched bed, might well have cringed, too.