If you were looking to retell the story of one of the great lovers in Greek myth, you could choose Paris, whose love (or lust) for Helen launched a thousand ships against his city of Troy, and wiped it from the map. Or Orpheus, whose devotion to Eurydice led him down into the depths of hell to try to reclaim her. Or even Alcestis, who loved her husband Admetus so much that she was willing to die in his stead.

Probably the last mythical figure you might try to rework as a romantic hero would be Achilles, a one-man genocide whose defining characteristic is his unquenchable anger. Achilles withdrew from fighting at Troy because Agamemnon had slighted his honour, and watched his fellow-Greeks being slaughtered by the Trojans; he only returned to battle when his friend Patroclus had been killed.

His revenge on Hector was then merciless: not only did he kill the bulwark of Troy, he dishonoured the corpse, dragging Hector’s body around the city three times. Homer sets all this out in the opening line of The Iliad: Sing, muse, of the wrath of Achilles. Even after death, his ghost still thirsts for blood, and Polyxena, a Trojan princess, has to be sacrificed at his tomb before the Greeks can sail home from Troy.

But Madeline Miller has found the lover beneath all the bloodshed and fury, and The Song of Achilles is an achingly beautiful book. It is told from the perspective of Patroclus, Achilles’ close friend and lover. Exiled by his father to live in the court of Peleus, Patroclus soon falls in love with Peleus’ son, the superhuman Achilles: from childhood, his demi-god status means he is swifter, more beautiful and more skilled than all his peers.

Astonishingly, to Patroclus’ eyes, Achilles returns his love, and the two boys grow into adulthood and a love affair. Achilles never ceases to be a godlike figure to Patroclus, ‘Then I turned to look at him. He was on his side, watching me. I had not heard him turn. I never hear him.’

Miller’s prose is more poetic than almost any translation of Homer you’ll ever read. Iphigenia, sacrificed by her father Agamemnon to appease the goddess Artemis, is described as having ‘A tripping name, the sound of goat hooves on rock, quick, lively, lovely.’ And when Briseis, the concubine Agamemnon later steals from Achilles, gradually learns Greek from Patroclus, ‘Her words were like new leather, still stiff and precise, not yet run together with use.’

The sense of impending tragedy is never far away from these lovers. Achilles has long known that he must choose between a short, glorious life, and a long one lived in obscurity. Miller ramps up the dramatic irony inherent in their story: both men know that Achilles will never return from Troy, that he is fated to die there. But Patroclus is too obscure to figure in prophecies, so he dreads the horror of life after Achilles’ death: ‘I rose and rubbed my limbs, slapped them awake, trying to ward off a rising hysteria. This is what it will be, every day, without him. I felt a wild-eyed tightness in my chest, like a scream. Every day, without him.’

We know, as Patroclus does not, that he must die before Achilles does. And only once Patroclus is dead does the truly terrifying aspect of Achilles’ nature come to the fore. When he finally faces Hector, the latter asks that his body be returned to his family, when Achilles is done with him. ‘Achilles makes a sound like choking. “There are no bargains between lions and men. I will kill you and eat you raw.”’

Miller spent ten years writing this book, yet her deft prose conceals the hard work and painstaking research which she has clearly put into it. This is a deeply affecting version of the Achilles story: a fully three dimensional man – a son, a father, a husband and a lover - now exists where a superhero previously stood and fought.