Adler & Gibb, the play by English experimental theatre master Tim Crouch, is a proverbial riddle, wrapped in a mystery, inside an enigma. The piece, which premiered at the Royal Court Theatre in London two years ago, is ostensibly about two conceptual artists from New York City, named Janet Adler and Margaret Gibb.

The collaborative artists have numerous, well-known artworks to their names, as well as established personal histories and their own website (adlerandgibb.com). Yet they don't exist.

What does exist, as Summerhall venue audiences will discover during the forthcoming Edinburgh Fringe, is a drama that calls into question society's attitude to art and artists. In particular, the play challenges the obsession with "authenticity", which hangs like an ironic cloud over works of artistic imagination.

This is not the first time that Crouch – who is equally accomplished as a theatre writer, director and performer – has alighted on the visual arts as a theme for his special brand of unconventional theatre. During the 2007 Fringe the dramatist premiered England – a remarkable work about the contemporary art market, global inequality and medical ethics – at the Fruitmarket Gallery.

The genesis of Adler & Gibb, Crouch tells me, lies in his thinking, five or six years ago, about the brief, intense love affair between the great Irish playwright Samuel Beckett and the famous American art collector Penny Guggenheim (which Crouch describes as "a day in bed together"). However, when he came to write on the subject, Crouch realised that he couldn't create a character for Beckett.

Nevertheless, there was something in Guggenheim's place in the New York visual art scene that drew him towards a different kind of play. The commercialisation and commodification, not only of the art work, but also of the artist, suggested the characters of Adler and Gibb.

Following Adler's death in 2004, the proverbial merde hits the fan. The pair's famously "uncompromising" work becomes impossibly compromised. The home they shared together is invaded by filmmakers who allow nothing, not even Gibb's unexpected presence in the house, to derail their narrative of Adler's life and work.

The motivation for this desecration is, of course, commercial gain. "A lot of money is being made from artists who wanted to disconnect from the commercial world," says Crouch.

The filmmakers' arrival in Adler and Gibb's home is, he says, "a raid". Indeed, Gibb leaves them in no doubt as to her feelings about their activities, as she cries: "Stop thief! Help! Rape! Rape!"

"There's a pillaging of an identity," Crouch suggests, "the pillaging of a life and the pillaging of a principle, all for the sake of making money."

As so often with Crouch, whatever the declared subject matter, the play also makes its way around to the subject of performance itself. The destructive biopic of Adler within the drama came from thoughts he had early in the process of writing the piece.

"A story emerged about an actor pretending to be another person," he explains. "It felt very prescient, it was around the time that Daniel Day-Lewis was winning Oscars for Lincoln.

Crouch was, he says, responding to, "the fetishisation around authenticity and character, and the dubious political aspect of trying to own someone's life."

No-one who knows Crouch's work will be surprised to learn that Adler & Gibb does not have a straightforward narrative or a conventional theatrical structure. In many ways the dramatist is the antithesis of Hollywood filmmakers, like Spielberg, who ask us to believe that they are creating "authentic" representations of reality.

Crouch, by contrast, follows what he calls his, "desire to loosen the threads around how we represent reality." One way in which he does this is by including in the play the character of an eight-year-old girl who switches objects around.

"A gun becomes a branch of a tree. A spade becomes a child’s windmill. At one point, a gun and a sledgehammer are both substituted by plastic lobsters."

If the girl in the piece plays fast and loose with the objects, Crouch himself has intervened just as radically in his production. The show that opens at Summerhall next week (and that will go to Los Angeles next year) is a very different beast from the one that was staged at the Royal Court in 2014.

The play has been substantially rewritten. The piece now has a different cast and a different set.

"There's a work of art by Adler and Gibb called There Are Now Enough Objects," Crouch comments. "I just felt that we didn't subscribe to their philosophy two years ago."

Edinburgh audiences will be offered a new, stripped back Adler & Gibb, a show in which Crouch and his team have, "taken a lot of stuff away so that we can add more theatre."

Adler & Gibb is at Summerhall, August 3-27. For further information, visit: festival16.summerhall.co.uk

FESTIVAL HIGHLIGHTS

Richard III

Royal Lyceum, Aug 24-28

I had the good fortune to catch this spellbinding production, by leading German director Thomas Ostermeier, at the Shakespeare Festival in Craiova, Romania earlier this year. Imagine the angry, sarcastic comedy of the late Bill Hicks combined with the punk sensibility of Iggy Pop and you're getting close to actor Lars Eidinger's high-octane characterisation of Shakespeare's famous "hunchback". With the assistance of an illuminating microphone on the end of a bungee cord, the show focuses brilliantly on Richard's conspiratorial relationship with the audience. Dark, brooding and comic, this piece by the Schaubuhne company of Berlin is bound to be a highlight of this year's Edinburgh International Festival.

My Eyes Went Dark

Traverse, Aug 4-28

The 107 Group present what promises to be one of the most powerful dramas of this year's Fringe. Outstanding actors Cal MacAninch and Thusitha Jayasundera perform a two-hander about a Russian architect who is driven to an act of revenge after his loved ones are killed in a plane crash. Inspired by real events, the piece was critically acclaimed when it opened in London last autumn.

Once...

Assembly George Square, Aug 4-29

Derevo, Russian masters of elegiac physical theatre, revive their celebrated contemplation of the exhilaration, anguish and profundity of love. Like their compatriots Akhe and Song Of The Goat Theatre from Poland, Derevo have enriched the Fringe with their theatrical poetics over the years. Expect something beautiful and deeply emotionally engaging.

Under Ice

Summerhall @ the King's Hall, Aug 8-22

Written by German author Falk Richter and staged by well-known Lithuanian companies Arturo Areimos teatras and Oskaro Korsunovo teatras, Under Ice exemplifies the internationalism of the Fringe. A "poignant and intimate insight into the maladies of corporate life", Richter's play is concerned with capitalism's capacity to reduce people to mere functionaries of an economic system. Don't bother inviting Sir Philip Green, as the BBC was told last week, "he's on his yacht".

Leaf By Niggle

Scottish Storytelling Centre, Aug 4-28

Edinburgh-based Puppet State Theatre Company present their much-loved show based upon JRR Tolkien's short story. It is the tale of Niggle, the distracted painter who feels compelled to keep returning to the same painting of a tree and a landscape. Performed on an opulently designed set by Richard Medrington, the play boasts a soundtrack by Karine Polwart and Michael John McCarthy. A theatrical world of imagination beckons.