INTRODUCTION Among my most treasured books as a child was a volume of Greek myths. My eldest brother, a sleep-deprived junior doctor at the time, bought it for me from a warren-like bookshop near his fl at in London. The shop, sadly, is long gone, but I still have Children of the Gods , by Kenneth McLeish, illustrated by Elisabeth Frink. It infiltrated my childhood imagination - it was one of the things that set me on the path of studying classics, and becoming a writer. Perhaps it was those pictures, those muscular pencil drawings, that made the greatest impression: Artemis, with her lean, athletic body; Hades, inscrutable king of the dead, magnificent and horrifying in his chariot, eyes shadowed by his dark helmet. Of course, the stories were marvellous too, strange and wild, full of powerful witches, unpredictable gods and sword-wielding slayers. They were also extreme: about families who turn murderously on each other; impossible tasks set by cruel kings; love that goes wrong; wars and journeys and terrible loss. There was magic, there was shape-shifting, there were monsters, there were descents to the land of the dead.

Humans and immortals inhabited the same world, which was sometimes perilous, sometimes exciting. The stories were obviously fantastical. All the same, brothers really do war with each other. People tell the truth but aren''t believed. Wars destroy the innocent. Lovers are parted. Parents endure the grief of losing children. Women suffer violence at the hands of men.

The cleverest of people can be blind to what is really going on. The law of the land can contradict what you know to be just. Mysterious diseases devastate cities. Floods and fi re tear lives apart. For the Greeks, the word muthos simply meant a traditional tale. In the twenty-first century, we have long left behind the political and religious framework in which these stories first circulated - but their power endures. Greek myths remain true for us because they excavate the very extremes of human experience: sudden, inexplicable catastrophe; radical reversals of fortune; seemingly arbitrary events that transform lives. They deal, in short, in the hard basic facts of the human condition.

For the ancient Greeks and Romans, myths were everywhere. The stories were painted on the pottery that people ate and drank from; they were carved into the pediments of the temples outside which they sacrificed to the gods; they were the raw material of the songs they sang and the rituals they performed. Myths provided a shared cultural language, and a tentacular, ever-branching network of routes towards understanding the nature of the world, of human and divine life. They explained the stars. They told of the creation of plants and animals, rocks and streams. They hovered around individual locales, explaining the origin of towns, regional cults and families. They reinforced customs and norms - sometimes offering a narrative justification for habits of oppression, not least of women and outsiders. For a people scattered liberally across the Mediterranean and the Black Sea - Greek culture flowed out well beyond the boundaries of the modern Greek state - they also provided a shared sense of cultural identity.

The tales in this book draw on sources by people writing not only in Greece, but in what we would now call Algeria, Libya, Egypt, Turkey and Italy. The world they filled with stories stretched from Greece to Georgia, from Spain to Syria, from Afghanistan to Sudan. The Greeks often took a sceptical attitude to their own myths. The earliest philosophers questioned whether the events described in the old stories could really have happened. But even the staunchly rational Plato at times invented his own legendary stories to drive his philosophical points home. From him we have the idea of the lost city of Atlantis, and his Republic famously ends with the ''myth of Er'', a haunting and strange story of the journey of human souls after death. No one could do without myths. What we think of as ''the Greek myths'' are the stories we find in the poetry, plays and prose of the ancient Greeks and Romans - a world also animated by an extraordinary surviving visual culture including ceramics, sculpture and frescoes.

These myths deal with a long-lost past in which the worlds of immortals and humans overlap, and in which some exceptional humans can become almost divine. It is from this vast, contradictory, extraordinarily variegated body of literature that the tales in this book are taken. Greek literature begins with the Iliad and the Odyssey , epic poems committed to writing somewhere between the late eighth and sixth centuries BCE, but drawing on a centuries-old oral tradition. These works, traditionally attributed to Homer, narrate stories from the Trojan War and its aftermath - versions, perhaps, of dimly remembered conflicts that took place in around the fourteenth to twelfth century BCE. At about the same time as the Homeric epics were written down, a Boeotian author called Hesiod produced his poem Theogony , which describes the origin of the gods and of human life. Homer and Hesiod provided the Greeks with a bedrock of literary mythical stories. But they were just the beginning. Myths appear in a dizzying range of literature: the Homeric Hymns , for example; songs dedicated to different Greek gods, traditionally attributed to Homer, but almost certainly written at later dates.

Then there are the Odes of Pindar, composed in the early fifth century BCE as victory poems for winners of Panhellenic religious sporting contests, and drawing on mythical stories for their poetic force. The great tragedians of fifth-century BCE Athens - Aeschylus, Sophocles and Euripides - almost invariably took stories from myth as their material. Later, in the great seat of culture and learning that was Alexandria, one of the cities established by Alexander the Great after his conquest of Egypt in 332 BCE, Apollonius of Rhodes wrote his epic poem Argonautica about Jason''s quest to retrieve the Golden Fleece, and Callimachus wrote his myth-infused Hymns . The Romans inherited the story-world of the Greeks'' myths, absorbing and expanding it with their own distinctively flavoured narratives. Some of the stories I tell are, strictly speaking, Roman myths. Virgil''s epic poem the Aeneid , which he was still working on when he died in 19 BCE, established a grand mythological origin for Rome; it was meant as both homage and rival to the poems of Homer. Metamorphoses , by Virgil''s much younger contemporary Ovid, was finished around twenty years later. Mythical stories tumble out of that poem in almost bewildering profusion; it is the most brilliant ancient treasury of classical myths that survives to us.

From later on in the Graeco-Roman period, ''handbooks'' of myths survive, prose volumes furnishing the reader with a guide to the most important stories. The best and most important of these, drawing on many early sources that are now lost, is the first- or second-century CE Library , by a writer known, somewhat confusingly, as Pseudo-Apollodorus. (The work was once attributed to a second-century BCE scholar called Apollodorus of Athens, but no longer, hence the prefix.) Also in Greek was the Dionysiaca , its subject the exploits and journeys of the god Dionysus. A vast, baroque and, I have to admit, sometimes exhausting work (the length of the Iliad and Odyssey combined), its author was Nonnus, who lived in the Greek city of Panopolis in Egypt in the fifth century CE. It may sound paradoxical, but other important sources are those stories that no longer exist in their entirety. The works of Homer were once part of an ''epic cycle'' that also contained long poems about the parts of the Trojan War not described in the Iliad , and about the deep past of Thebes, among other tales. These remain to us only as precis, mentions in other works, and brief fragments.

In the case of tragedy, during the fi fth and fourth centuries BCE Athens produced around a thousand plays by as many as eighty authors. Only thirty-two of them survive in full. Scholars, with patient, detective-like skill, have reconstructed what they can of lost works, drawing on fragments of ancient papyrus found in Egypt, assembling tantalising hints of a lost world of stories. There was no canonical, fully authoritative account of ''the Greek myths'' in antiquity. There were certainly versions of stories that dominated. Euripides'' version of the Medea story, for example, became extremely popular, and you can see its famous final scene - the titular character magnificent in her dragon-drawn chariot - painted on Greek pots. But stories of the Greeks were endlessly variable, endlessly proliferating. It would be an impossible, Casaubon-esque task to gather all of their madly tendrilling versions into a single volume.

The dizzying variety of stories reflects the geography, politics and culture of the Greek world - scattered over a mountainous mainland, a jagged coastline, hundreds of islands, and the western seaboard of what is now Anatolia. From the eighth century BCE onwards, expanding trade networks also led Greeks to settle around the Black Sea, and on the coasts of North Africa, southern France and Spain. The same goddess might come with different associations, and differently weighted stories, in different city states. (The city-state, polis , was the typical political unit of the Greek world. The thousand or so poleis were culturally distinctive in all kinds of ways and were often at each.