With the summer blockbuster shows already open at the National Galleries of Scotland's Queen Street and Belford Road venues - Man Ray is at the Portrait Gallery, Witches & Wicked Bodies at Modern Two - it was left to Peter Doig to provide the flagship exhibition at this year's Edinburgh Art Festival, which launched on Thursday.

Peter Doig: No Foreign Lands is at the Scottish National Gallery and marks a homecoming of sorts for the 54-year-old painter: he was born in Edinburgh, a capital connection reflected in the exhibition's title which is taken from Robert Louis Stevenson's 1883 travel memoir The Silverado Squatters. In fact, the Doig family left Scotland for Trinidad when Peter was three, and later moved to Canada, where he grew up and which also claims him as one of its own. No matter.

He arrived in London in 1979 to study art and now divides his time between there, New York, Dusseldorf (where he teaches) and Trinidad, which he made his home in 2002 and which features in many of the paintings here. The other notable fact about Peter Doig is that he holds the sale record for a work by a living European artist - his 1991 painting The Architect's Home In The Ravine went for a shade under $12 million at auction earlier this year.

As the artist himself said at Thursday's press view, this is a survey rather than a retrospective. Tate Britain undertook that second task in 2008. So here we have the fruits of the last decade's work, running more or less chronologically through the RSA building's grand halls, though the eight rooms are given thematic titles such as Figures and Geometrical Structures (Doig likes to paint square and oblong grids over his landscapes, as if in an attempt to tame the wild greenery or perhaps in a gesture to landscape painting itself).

The work, mostly monumental in scale, suits the venue. Doig's brush brings us close to the lush Trinidadian countryside, though always filtered through his many other preoccupations: memory, the ambiguity of memory, art history, photographs (his own and other people's) and films. When an image from horror flick Friday The 13th lodged itself in Doig's brain it found expression in the painting 100 Years Ago (Carrera), which shows a ghostly figure in a long red canoe with a tropical island in the background. One room in the show, meanwhile, is given over to the handpainted posters he makes for a film club he runs in Port of Spain.

Another preoccupation of Doig's is fusing his own experiences with other people's, often across space and time. One example is Pelican (Stag), perhaps the most familiar painting in the exhibition. It shows a walking man, half-turned to face the viewer, lit by a shaft of light coming down from a palm tree. It's based on a scene Doig witnessed while walking on a beach in Trinidad with his friend Chris Ofili - a man killing a pelican then dragging it away - but it has been parlayed into art by means of a photograph Doig found of a fisherman in India hauling a net along the sand. Something similar happens in House Of Pictures, which shows a man looking in a gallery window. Doig used two photographs to make the painting, one which he took in Vienna (the gallery) and another he found in an archive, of a man in Vancouver. It's a mischievous comparison, I admit, but in the enigmatic scenes Doig often presents, it's hard not to be reminded of the work of another collectable Scottish painter - Jack Vettriano.

At the effortlessly swish Ingleby Gallery, London-based artist Peter Liversidge has a show called Doppelganger. At its core is a suite of 10 etchings published by German artist Max Klinger in 1881. They tell the story of how Klinger finds a long, white woman's glove in a Berlin skating rink and then places the glove, an erotic item in its own right, into a series of tableaux which are alternately dreamlike and nightmarish. You don't need to be Sigmund Freud to know there's a psychosexual urge at the heart of it all.

Liversidge explores all this by means of a re-creation of what he thinks Klinger's front room might have looked like if the German had framed his own etchings, and (upstairs) by a series of large-scale facsimiles of them. In front of five of these, carved from sexy white Carrera marble, is a facsimile of the glove, though interestingly one of them has a clenched fist. Even more playful, the exhibition includes Liversidge's initial proposals for each of the pieces, addressed to the Ingleby Gallery and typed out on an old manual typewriter. In this work, the curators get folded into the story too. It's a neat move.

At Inverleith House, Mostly West celebrates not a collaboration between artist and curator, but those between artist and artist and artist and viewer. Here, each is anchored by the participation of late Austrian artist Franz West. It's the first exhibition of works by him consisting only of these collaborations, and among the artists featured are Douglas Gordon and Sarah Lucas. The viewer is also expected to be a collaborative participant. Typically for an Inverleith House show, it's difficult work and the venue makes no apologies for the fact. Bravo.

The result of another collaboration, this one between Scottish artist Christine Borland and Berlin-based American Brody Condon, can be seen in New Calton Burial Ground where it forms part of the Parley series of Art Festival commissions. The title is well chosen: it means discussion, but it also gestures to the name by which the Scottish Parliament is colloquially known in the capital.

The Borland-Brody piece is sited in the cemetery's 19th-century watchtower and, happily, overlooks Enric Miralles's landmark building. It's called Daughters Of Decayed Tradesmen and it's based on interviews conducted with aged female twins who were among the last residents of the Trades Maiden Hospital, founded in 1704 to educate the daughters of "decayed" tradesmen, hence the title.

These memories have in turn been rendered as binary code on cardboard sheets which replicate those used by the Jacquard Loom, a 19th-century loom housed in the National Museum of Scotland. The sheets are stitched together into two long, looping strips, one for each twin, which hang down from the ceiling. Context is all, here: you need that knowledge to make sense of the work. But if the wind's up - and when is it not on this exposed hillside? - the inscrutable strips will dance in the breeze and make their own display, regardless of the meaning the artists have given them.

Another in the Parley commissions of outdoor works is Ross Sinclair's Real Life And How To Live It In Auld Reekie, the latest chapter in his ongoing (and long-standing) Real Life series. Mostly they take the form of billboard "top 10" posters scattered across the city, listing (variously) Edinburgh footballers, writers, Enlightenment figures, artists and bands. There are also beer mats (find them if you can, pubgoers).

To end, then, a vignette: as a Japanese tourist tries to photograph a seagull next to the Scott Monument, two blue-rinsed Edinburgh ladies stop by the list of 10 fictional Scots Sinclair has hung on the railings there. One of them starts reading from the top. "Shrek," she says. By the time she gets to Groundskeeper Willie from The Simpsons, her lips are pursed and she is truly baffled. It's not, perhaps, what artists mean when they talk about "an intervention", but it highlights the growing brio and resourcefulness of this latest addition to the capital's summer festivals.