If you were lucky enough to read Latin at school the chances are you will remember a bit of Catullus: the best thing by far about the slog of amo, amas, amat is that you get to read, after just a year or two, what one Latin teacher described to me as "pretty hardcore literature". Often this arrives in the form of a Catullus poem: perhaps "Passer, deliciae meae puellae" ("Sparrow, my girl's darling"), a funny, erotic, tender piece about his lover's pet bird; or the wonderful, paradoxical, agonising two-liner "Odi et amo. quare id faciam, fortasse requiris? / nescio, sed fieri sentio et excrucior." ("I love and I hate. Why do I do this, perhaps you ask? I don't know, but I feel it happening to me, and I am in agony.")

The first time I read poems like these I understood the reason for learning such a remote and frankly difficult language, with its endless necessary rote-learning, its phalanxes of endings, its brain-bending complexities of grammar. I felt as though I had been given the key to a subversive, exotic, urbane world. Catullus invented love poetry: that is, he was the first classical poet to write about relationships. The Greeks had written wonderfully about desire - think of the emotionally acute, limpid, supple, verses of Sappho. But it was Catullus who mapped out the peaks and troughs of romance: the breathless preludes, the heart-in-mouth anticipation, the joy, the disappointments, the heartbreak, the gruelling clamber back to sanity. About a quarter of his corpus of just over 100 poems is about his relationship with one woman: Lesbia. Rereading these works, I came to realise how pin-sharp Catullus is in his articulation of the trials of love.

Catullus' most substantial work, however, is his poem 64 - a miniature epic, or epyllion, and by far the longest and most ambitious of his poems. For me it's one of the greatest works of literature ever produced.

Catullus 64 is full of tricks and false turns, paths that wind back on themselves, and red herrings. At its heart is the story of Ariadne, who helped Theseus kill the minotaur in the labyrinth of Knossos, and whom Theseus abandoned on the deserted shore of Naxos. It's fitting, then, that the structure of this poem is like a labyrinth, and not a neat, formal labyrinth full of comforting symbolism, but the sort that we can recall from our dreams, one that it would be extremely discomfiting to get stuck in.

When the poem opens, there's no clue as to what awaits us at the centre of the maze:

The noble pine trees bred on Pelion's top
Once swam, they say, through Neptune's sliding element
As far as the river Phasis and the realm
Of King Aeetes; that was when the pick
And pride of the young Argive chivalry
Burning to loot the Golden Fleece from Colchis,
Dared the salt depths in their impetuous ship,
Churning the blue to white with firwood blades.

Catullus' swimming pines are the Argo (the circumlocution hints towards the notion that it was supposedly the first ever ship; it's a knowingly naive description as if from someone who'd never seen one before). This, you think, is going to be a poem about Jason and the Argonauts. A reader in the first century BC might have noted the references to the chic Hellenistic poem "The Argonautica", by Apollonius Rhodius, and be expecting a retelling of the story of the capture of the Golden Fleece, Jason's encounter with Medea and so forth.

Except that a few lines later, something disrupts that comfortable expectation. Catullus starts to describe an episode that occurred en route.

When her beaked prow cut the surge
And the waves, oar-wounded, whitened, the sea-nymphs
Peered out of the gullies of the foam,
Amazed at the apparition. Never before
Or since have men's eyes seen the Nereids
Stand nipple-naked in the grey-green swell.
That was the moment, so the story goes,
When Peleus looked and loved, and Thetis happily
Stooped to an earthborn mate, and even Jove
Acknowledged in his heart that they should wed.

Peleus, mortal hero and Argonaut, meets Thetis, sea goddess: love at first sight. The poem, instead of continuing to Colchis and the Golden Fleece, unexpectedly cuts back to the home of Peleus, in Thessaly.

Now follows a gorgeous description of lavish wedding celebrations. Catullus draws us ever further into the house. Right at the centre is a hall with a bed and on the bed is a coverlet, embroidered with "figures / of antique times marvellously representing / Heroic enterprise". You might expect something rather martial from that description - what we actually "see", though, is an embroidery of Ariadne, abandoned on the shore of Naxos by Theseus, whom she was expecting to marry.

Here Ariadne
On the surf-booming shore of Naxos gazes
At Theseus and his shipmates making off
And, still incredulous of what she sees,
Feels love, a wild beast, tear at her ...

She is trapped in time, just at the moment when she realises the appalling situation she's in. One of my most treasured possessions is a small 18th-century drawing of this scene, or to be precise the scene seconds before: Ariadne is yawning and stretching on her al fresco bed on Naxos, and you can just see Theseus's ship halfway to the horizon.

But, unlike my drawing, Catullus's embroidery appears to have sound effects - "fluentisono" is the marvellously abstruse word translated here as "surf-booming". Soon the picture moves, too, and Ariadne speaks, cursing her faithless lover, a model for the curses Dido rains down on Aeneas in Virgil's Aeneid. Ariadne is taking over the poem, breaking out of the embroidery and becoming - perhaps - what Catullus 64 is really all about. The poem flashes back to what happened on Crete: how Theseus turned up as one of the seven Athenian youths annually sacrificed to the Minotaur, how Ariadne fell in love with him, and decided to help him by giving him a sword and a ball of thread. Then the story flashes forward to Theseus's return to Athens. He told his father he'd hoist white sails if he was coming back alive, but he forgot (just like he forgot about Ariadne). His father, assuming he was dead, threw himself from the Acropolis and dashed himself against the rocks.

The technique of describing a work of visual art in a poem is known to classicists as "ecphrasis". The first example of this trope is the description of the shield of Achilles in The Iliad book 19; there are many others. Catullus, it seems to me, is playing around with the notion of what art can do: a masterpiece of embroidery can, perhaps, come alive in our imagination, break free of its threads, suck us right into its reality. But of course we're not really looking at an embroidery; we are reading text. At one point Catullus even leaps further into the maze: he describes Ariadne as like a statue. So we've a sculpture within an embroidery within a poem.

So far do we accompany Catullus as he digresses and manipulates time, that we forget he's describing an artwork within an artwork. So it's a shock when he writes "ac parte ex alia florens uolitabat Bacchus" - "another section of the coverlet / Showed virile Bacchus swaggering". Oh, you think - it is a textile after all, just a bedspread. It's a little like that other famous artwork-within-an-artwork involving Ariadne - Strauss's Ariadne Auf Naxos. In that story, the character of the Composer writes a grand opera about Ariadne, into which he is instructed to introduce figures from commedia dell'arte. The genre clash between the tragic Ariadne and the commedia dell'arte pranksters reminds us constantly of the artifice of the inner opera, and so of the work that frames it, but when the Ariadne character sings, you can't help but get caught up in the power of her emotion.

"Ac parte ex alia": this section of the embroidery shows what happens next - Ariadne is rescued by the god Bacchus, who has fallen in love with her from afar. It's another description that breaks free of its artistic confines: this is a very noisy embroidery. The entourage "tereti tenuis tinnitus aere ciebant", "stretched fingertips to tattoo the tambourine". It's a scene given vivid visual life by Titian, in his Bacchus and Ariadne, in the National Gallery.

We leave Ariadne to her happy ending, and turn back to the party chez Peleus. The Fates appear to sing a wedding song, foretelling a happy marriage for the couple, and the future of their son, Achilles. But it is actually rather horrific: the Hellespont will be dyed red and made warm by the slaughter Achilles wreaks in the Trojan war, they sing.

Finally, at the end of the song, there's a kind of epilogue. Suddenly all the preceding narrative is placed in a sort of Golden Age: "For then, before religion was despised, /The sky dwellers in person used to visit / The stainless homes of heroes and be seen / At mortal gatherings." It's as if the poem has whooshed us forwards through time. So far, we've been involved in the story as if it's taking place quite immediately; now we're abruptly reminded that it happened aeons ago, and we're invited to look back on what we've just read as if from a great distance. Moreover, it is the sins of man that have brought those glorious, antique days to an end - it is because of our greed and impatience, our adulteries and iniquities that the gods no longer visit men, "nec se contingi patiuntur lumine claro", "or care to endure / The touch of our too glaring light of day."

It's hard to know how to take this disturbing ending, with its indictment of modern mores. As for its puzzling tone: is it macabre and playful, or macabre and deeply serious? There's no telling if we have escaped the labyrinth, or are trapped there, eternally hesitating between forking paths.