Michelangelo's Dream, Courtauld Institute, London

A breathtaking collection of drawings outlines the intriguing back story of the artist's dangerous desire

That Michelangelo was a tricky customer is borne out by contemporary reports of him. To the 16th-century art historian Vasari, whose opinion has stuck, he was il divino, made by God as a model of how men should be in all things: poetry, art, bodily beauty.

To a viewer of the newly-painted Last Judgement fresco in the Sistine Chapel, Vasari's divine Buonarroti was an inventor delle porcherie, a maker of porkery, of obscenities. How can two such different – two so opposed – Michelangelos have co-existed?

Which brings us to Tityus, to Christ and to Tommaso de' Cavalieri. Tityus was a mythological Greek giant whose future as a rapist was assured when he tore his mother's womb with his own phallus. (A species of large-horned beetle is named after him.) Fully grown, Tityus tried to rape Leto, mother of Apollo, for which he was condemned to an eternity in Hades with vultures pecking at his liver: this is the subject of a drawing, The Punishment of Tityus, lent by the Queen to the Courtauld Gallery's fine new show, Michelangelo's Dream. Although the show's title is taken from another drawing – Il Sogno, or The Dream of Human Life, in the Courtauld's own collection – Tityus is its centrepiece. Shown in a two-sided vitrine in the middle of the room, it depicts, recto, the lustful giant writhing handsomely on a rock. Verso, Michelangelo has traced a figure which follows Tityus's outline almost exactly. It is of the newly risen Christ.

To artists of the High Renaissance, Christ's dual nature as human and divine dovetailed neatly with courtly thoughts of profane and sacred love. He may have been God but He was also Man, prone to the same fleshly urges as Tityus. This two-sidedness had particular appeal for Michelangelo, thought to have been homosexual at a time when sodomy was punishable by burning. In 1532, the artist, then 57, met a beautiful 23-year-old Roman nobleman called Tommaso de' Cavalieri. It seems, for Michelangelo at least, to have been love at first sight. The question was which kind of love, and how to express it safely.

One way was to send Tommaso carefully encoded sonnets, the manuscripts of some of which are included in this show. Michelangelo writes of his beloved as a fire in which he, an ageing phoenix, will be reborn: any suggestion of sexual inflammatoriness can be explained away as poetic licence. Another way of declaring his love for Tommaso was in so-called "presentation drawings" – finished works meant for intimate consumption, to be handled and treasured by their recipient. Tityus is one of these, as is the titular Dream. Both use male beauty to express spiritual awakening. Indeed, as with the image of the phoenix, both find salvation in male flesh.

All of which makes the anonymous attacker of Michelangelo's porcherie arguably a more astute critic of art than Vasari. The dozen drawings by the artist in this perfect little exhibition show a tendency to knottiness, to figures which wind around each other and contort. This is a symbol, conscious or not, of the complexity of their meaning, their levels of encryption. Any suggestion that Michelangelo's feelings for Tommaso might have been base – which is to say sexual – could be countered by noting that even the famously priapic Tityus has been given a tiny winky. For the more lustful thoughts Michelangelo may have harboured for his young hero, we have to look at the drawing of Phaëton he made a year later.

Son of the sun god, Helios, Phaëton insisted on driving his father's chariot, lost control of it and was killed by Zeus. It is a story of mortal presumption, and may suggest Michelangelo's own temerity in daring to woo the god-like Tommaso. What is beyond doubt is that the composition's focal point is on the genitals of a horse, then, as now, a byword for virility. Tommaso's surname, Cavalieri, means horseman in Italian, from cavallo or horse, which is also slang for crotch. It seems clear that Michelangelo both hoped and feared that this allusion would be seen by Tommaso, that part of the power of this exquisite drawing – of all the presentation drawings – is that, like Phaëton, they dice, quite literally, with death. Did Tommaso, soon to be a husband and father, spot this meaning, and if so, did he care? Who can say. Tradition has it that he was holding Michelangelo's hand when the old man died in Rome in 1564.

To 16 May (020-7848 2526)

Next Week:

Charles Darwent goes to a Tate Britain show that challenges one view of Henry Moore: that he is father of the turd-in-the-plaza school of sculpture