Hansel is a little slip of a girly-boy born to a West German mother and an American G.I. father. When the Wall is erected, his mother moves the two of them to a tiny, cramped apartment in East Germany, saying, "It is better to be powerless". One day Hansel follows a trail of American candy through the woods. The trail leads him to his sugar daddy - a handsome black American G.I. named Luther. In order to marry Luther and leave East Germany, Hansel adopts his mother's name - Hedwig - and has a sex change. As his mother says, "To be free, you have to leave something behind." But the operation is botched, leaving Hedwig with an inch of angry flesh.

So begins this remarkable glam-rock-opera, an "anatomically incorrect rock odyssey". Hedwig And The Angry Inch is a cult film, like The Rocky Horror Picture Show meets This Is Spinal Tap, starring Kiki And Herb, directed by Todd Haynes. With a bit of Pink Floyd: The Wall chucked in. Hedwig's story is played out to loud, trashy songs inspired by those "crypto-homo rockers" David Bowie, Lou Reed and Iggy Pop.

Hedwig's search for someone to make her whole is based on a myth in Plato's Symposium, that lovers are actually two divided parts of the same being, longing to be unified. "Does my other half have what I don't? Did he get the looks, the luck, the love? Is it a he or a she?"

Packed with literary, filmic and musical allusions, it delivers more on repeat viewings (I know this because I've seen it two days running). It's great fun. The script is packed with bitchy one-liners: "When it comes to huge openings, a lot of you think of me", "I was involved in the very business we call show, performing odd jobs - mostly the jobs we call blow." When little Hansel tells his mother that "Jesus died for our sins," his mother snaps, "So did Hitler!" The jokes come thick and fast: the band's manager is named Phyllis Stein; they play at a women's rock festival called Menses Fair; Hedwig reveals she once wrote a philosophy paper titled "You, Kant, always get what you want".

Hedwig always looks fab: she gets to wear more than 40 costumes, and 30 different blonde wigs, looking variously like Marlene Dietrich, Debbie Harry, Farrah Fawcett, and Tina Turner. There's even one outfit made entirely out of wigs.

John Cameron Mitchell is brilliant as Hedwig. He also directs the film and wrote the screenplay. Stephen Trask wrote the songs. The rest of the cast is strong, though they don't get much of an opportunity to shine - this is Hedwig's show. But take a close look at Yitzhak, the bearded bassist (I'm not saying why).

It's appropriate that a film about the search for your other half should be in two distinct halves. After the glam riot that is "Wig In A Box", the film takes a dark, desperate turn, and loses its sure footing. The two subplots - one involving Hedwig's protégé Tommy Gnosis, the other involving Yitzhak's desire to become a drag queen - are insufficiently explored. The film ends with Hedwig walking, naked and wigless, into the night. Has she found her other half? Has she become he? Is the Tommy Gnosis character her other half? Or is Yitzhak? Has Hedwig realised she wasn't missing anything, and was always a whole? I don't know.

But I do know I loved the film, and I know I want to see it again.