Weight Jeanette Winterson Canongate, 151pp, £12 ISBN 1841956716 The Penelopiad Margaret Atwood Canongate, 199pp, £12 A Short History of Myth Karen Armstrong Canongate, 159pp, £12

Anyone with a child at primary school will recognise the assignment: "Retell the story of Hercules in a modern setting." Thanks to the national curriculum, this is how British children are introduced to Greek myth. One reason Canongate's new Myths series is an intriguingly risky project is that it sounds so much like that primary school task, but wants to take an altogether more adult view of how the old stories remain part of our culture. A list of starry writers has been commissioned to retell ancient myths for a modern audience, starting with Margaret Atwood on Penelope and Jeanette Winterson on Atlas. The great model of James Joyce's Ulysses looms forbiddingly over any such venture, and the potential for trivial burlesque or portentous symbolism is dismaying. But the first two novellas make real sense of the return to the ancient world. As well as being engagingly readable and surprisingly moving, both manage to find a modern heart in these old paradigms.

Jeanette Winterson's Weight retells the apparently undramatic tale of Atlas holding up the world. It would be easy enough to make Atlas a symbol of the burden each of us carries. This is perfect Winterson territory: the past weighing down crushingly on the developing self. But since nothing much happens to Atlas over the centuries, rather more is needed to spin a story out of the icon. Winterson finds it in Hercules, the archetypal he-man, who arrives and takes the weight of the world on his shoulders for a day. Her Hercules is a raping, raging, wanking, hyperactive go-getter. The vulgar humour of the portrait offsets the reflective passivity of Atlas, and the beautifully rhythmic prose in which his inward-looking life has been described. This interplay between ceaseless activity and constant stillness leads Winterson to reflect stirringly on the choice of whether or not to act: Hercules's endeavours lead him relentlessly to his fated death, while Atlas's gradual recognition of his own desire to shift the burden makes his passivity heroic.

The myth, however, is inexorably brought home to the here and now. Atlas meets and befriends Laika, the dog from the first Sputnik, circling in space. The narrative of Hercules and Atlas is gradually intertwined with that of the author's own life. Their heroic struggles become ways of exploring Winterson's attempts to shift the burdens of her past and take control of her life. This gives a particular charge to a pun that echoes in the title: the book is as much about the "wait" as "weight". Time weighs as heavily as the world on Atlas, and for Winterson the long wait to put down her burdens never quite ends. The book concludes with the hope that Atlas will put the world's mass aside and finally just walk away. But it remains only a hope.

Margaret Atwood's The Penelopiad presents Penelope, the wife of Odysseus and cousin of Helen of Troy, now in the Underworld and reflecting on her life (particularly as told in the epic poems of Homer). Atwood is more snide and boisterous than Winterson, and happily picks up the challenge of burlesque. Her Penelope is a slightly dippy hausfrau ("I stayed in our room a lot"), and her story is told in simple and deliberately naive prose ("Chapter XI: Helen Ruins My Life"). This is not the seering voice of Joyce's Penelope in the last chapter of Ulysses, but epic re-envisaged as bourgeois sitcom. Could the modern world ever replay epic without irony? Only with the Troy or Alexander of Hollywood, I expect.

Penelope's narrative is interspersed with song lyrics delivered by a chorus of maidservants. In the Odyssey, some of the maidservants of Odysseus's house start to sleep with the evil suitors while their master is away on his travels. When Odysseus returns and takes revenge on the suitors, the girls are punished with hanging. In Homer's memorable line: "They were strung up like little birds; they kicked their legs but not for long." Atwood allows these girls to tell their own story, and they come across as resentful but vivacious victims of the hero's desire for patriarchal order. (The novella could have been called The Handmaid's Tale.) They sing sea shanties, popular tunes and ballads. The chorus line kick their legs as if in a musical rather than in violent punishment.

Atwood, like the Coen brothers in O Brother, Where Art Thou?, relies on pastiche, light comedy and music for her reworking of the Odyssey. It contrasts strikingly with the darkness of Winterson's myth. Yet Atwood is also self- consciously exploring the role of ancient paradigms in modern life: comedy, too, gives us stories to live by. The book ends with a surprisingly poignant image, one that resonates with Winterson's thoughts on passivity and action: Penelope confesses that she is unwilling to risk going back to earth for another go at life - unlike Odysseus and Helen. Atwood carefully allows a glimpse of the real bravery it takes to escape from the unhappy sureties of bedroom and house.

Karen Armstrong's contribution to the Myths series is less successful. She has written perceptively and influentially on subjects as difficult as Jerusalem (a mythic city if any is). Here, given the task of writing a general introduction to the series, she has produced a book that will make any anthropologist embarrassed or angry. It tries to develop a history of the west from 20,000 BC to the present, divided into periods defined by types of myth. So Armstrong locates the origins of our myths in the Palaeolithic period, and traces their developments in the Neolithic period. Since there is not one scrap of evidence for any mythic tale in either period, this history does no more than develop its own myth about the distant past. Indeed, it is all-too-familiar a pattern: a fictional account of the past, told to make sense of the present. Unless I have missed some deep irony (a satirical expose of our fantasies about the past, perhaps?), Armstrong has been extremely misguided in the conception and production of this book.

Weight and The Penelopiad, however, can each be read in a short evening, and will give satisfying if contrasting pleasures. They bode well for the rest of the series - and for the continuing power of ancient myth over the modern imagination.

Simon Goldhill's most recent book is Love, Sex and Tragedy: why classics matters (John Murray)

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