Byron's memoirs were burnt by friends terrified of what they might contain. Ever since, biographers have been trying to make up for the loss. The attractions of the challenge are obvious. Not only was Byron a poet of the very highest rank - in every sense of the word - but he also led a life of incomparable scandal and glamour. The toast of a new era of mass readership, he was also its first and greatest victim. The parabola of his rise and fall retains its fascination to this day, for hooked as we are on the cult of celebrity, Byron's myth still serves as the archetype.

Myth can be dangerous for a biographer. Not the least of Benita Eisler's virtues is her sensitivity to the brilliance with which Byron fashioned his own image. His public posturing was only a part of this. Far more insidiously, from a biographer's point of view, he did it in correspondence and in "Don Juan", the greatest poem in English since "Paradise Lost". As Lady Byron ruefully acknowledged: "He is the absolute monarch of words, and uses them, as Bonaparte did lives, for conquest."

"Don Juan", Byron's masterpiece, is the most complete tribute that he paid to his favourite subject, himself - just like its author, it is dazzlingly mobile, infinitely various and virtually impossible ever to pin down. Yet it may be that in Benita Eisler the Napoleon of rhyme has at last met his Waterloo. This is the most perspicacious and convincing portrait of Byron I have read. It combines an instinctive sympathy for the power of Byron's self-dramatising with a refusal to do as so many other biographers have done, and either take it at face value or discount it altogether. Eisler is not the first to see the keynote of Byron's character as being "the sense that he had a special dispensation from the moral sanctions imposed upon others and a lifelong entitlement to the forbidden"; but no one has traced the implications of this before with such care and good sense.

The child of a marriage described here in its full squalid horror, Byron was raised in poverty before unexpectedly inheriting his noble title at the age of ten. In one sense this was, as Eisler puts it, "a fairy-tale sequence of events", yet in another it seems merely to have confirmed Byron's own belief in himself as the hero of his own melodrama. Crippled by a Calvinist sense of doom and literally by a club-foot, he was never to escape the shades of nightmare and romance that had darkened his childhood. In his adult life this was to provide him with the wellspring of his poetry, but it was also to doom most of his relationships, so that, as he said of his own father, "he seemed born for his own ruin and that of the other sex".

Indeed it is in its study of Byron's sexuality that Eisler's biography is most obviously superior to the biography that has until now been considered definitive, Leslie Marchand's three-volume study of the poet. Marchand chose to draw a discreet veil over the issue of Byron's homosexuality; Eisler, writing in more tolerant - or more prurient - times, feels no such compulsion. Many of the details she presents are fittingly sensational, but there should be no complaints about mud-raking: it is impossible to make sense of Byron's travels through Greece and Turkey, or indeed the breakdown of his marriage, without reference to the range of his sexual appetites. Eisler argues convincingly for Byron's sadistic and transvestite impulses, and does not shrink from the probability that, himself molested as a child, he in turn molested children.

She is candid, then, about his faults, even as she responds to all the qualities of charm and beauty that made him so irresistible. "He shone amid galaxies of brilliantly gowned and jewelled women. In gilt-framed mirrors he saw his slender, black-garbed figure and pale face multiplied, lit softly by thousands of candles reflected in the lusters of branching chandeliers." This is how Eisler opens her account of Byron's so-called "years of fame", when, after the publication of "Childe Harold", he was the undisputed lion of London society. It is by far the most impressive section. Other accounts of Byron's affairs during this period have tended to possess all the energy and danger of a bad Georgette Heyer novel, but Eisler has fashioned a narrative to rival Les Liaisons Dangereuses.

Describing Byron's first meetings with Caroline Lamb, she claims that they "have the symbolic quality of dance or dream". It is Eisler's achievement to give all Byron's relationships with women during the "years of fame" precisely such a quality. The dance - or nightmare - reaches its climax with Byron's doomed marriage.

Any biography of Byron must stand or fall by its interpretation of those terrible months. Eisler's own account is almost unbearably painful. She manages to retain our sympathy for both Byron and Augusta, the half-sister for whom he nurtured such passion, but the real triumph is her re- evaluation of Lady Byron. Usually presented as a humourless prig, she is here convincingly portrayed as a woman whom Byron could have loved. But he failed her - and in the end, like Frankenstein, did indeed create a monster. "If Byron had truly set out to corrupt his wife, he succeeded beyond his wildest dreams. He had turned her heart to stone."

Nothing in Eisler's narrative of Byron's exile quite measures up to her account of what had gone before. The final years of his life especially are underplayed; perhaps, in a fittingly Byronic way, Eisler was growing jaded. The judgements on the poetry, too, are disappointing: they are workmanlike, and not marked by the originality of perspective that characterises her understanding of the life. But set against the achievement of the book as a whole, any criticisms must rank as minor quibbles. I have never read a biography of Byron that made me regret less the destruction of his memoirs.

Tom Holland wrote a novel about Byron, "The Vampyre" (Little, Brown, £5.99)