A motorcyclist in black leathers is hurtling along an empty highway. In the distance a scorched red wilderness lies vast and flat. Suddenly he unclasps the handlebars and stretches out his arms until they appear, Christ-like, at perfect right angles to his body. It is a skilful feat of daredevilry, and it looks exhilarating — an earthbound approximation of flight. Welcome to the Australian outback.

This is Approach to Mundi Mundi (2007), an eight-and-a-half-minute film by the Australian artist Shaun Gladwell, who is also an expert skateboarder. A kind of bushman Easy Rider, it is the perfect introduction to the Royal Academy’s enormous new survey of Australian art, not least because it revels in the great outdoors and captures a sensation of soaring, sunny freedom — especially if, like me, you are greeted by it after walking down a drizzle-sodden Piccadilly.

Gladwell’s film also alludes to another exhibit in the show, which happens to be one of Australia’s most famous paintings: Sidney Nolan’s Ned Kelly (1946, see below), in which a black-helmeted rider, this time a 19th-century outlaw on horseback, gallops across an empty yellow plain towards scrub and an azure sky. Nolan and Gladwell both distil the principal theme of the RA’s exhibition: man’s heroic relationship with the thrilling but unforgiving Australian landscape.

How can a single exhibition encapsulate the art of an entire continent? Of course it can’t, but this one, organised in collaboration with the National Gallery of Australia, and featuring more than 200 works of art dating back to 1800, makes a pretty good fist of it.

After Approach to Mundi Mundi, the first gallery presents a display of modern indigenous art, representing a tradition stretching back tens of thousands of years before the first Europeans even glimpsed the Australian mainland at the start of the 17th century. This is a clever move on the part of the curators, since these enormous, dazzling paintings are far more exciting than the tight, narrow-minded little pictures from the early colonial period that follow — and which, if the exhibition’s chronological arc had been strictly adhered to, should have come first.

The indigenous pieces, rippling with constellations of abstract swirls, squiggles and stippled patterns using the red-and-ochre palette of Australia’s wild interior, are an Aboriginal equivalent of Op Art or gestural Abstract Expressionism, infused with ancestral magic. With the appearance of embroidered blankets and aerial photographs of the bush, they manage to be homely and universal at the same time.

The colonial work, presenting spick-and-span settlements like clones of European towns gracing Australia’s neatly tended coast, are the last word in bourgeois tedium. When Aboriginal “natives” appear in these paintings, they are silhouetted stickmen designed to lend a smattering of exoticism, reminiscent of the little devils and pitchfork-wielding demons that crop up so frequently in medieval Western depictions of Hell. If these works had opened the exhibition, visitors would be rushing back to Piccadilly in a trice.

Thankfully, as the 19th century wore on, artists working in Australia began to hit their stride, even if they were following movements that had already found favour in Europe. There are several grand oil paintings by the Vienna-born artist Eugene von Guérard, who arrived in Victoria in 1852. His Ferntree Gully in the Dandenong Ranges (1857) is an overwhelming composition anticipating The Day of the Triffids, in which rampant prehistoric ferns crowd the view like a horde of ferocious barbarians.

The later decades of the 19th century belonged to the generation of Australian Impressionists that included Tom Roberts, who studied at the Royal Academy Schools in the early 1880s, Frederick McCubbin, Arthur Streeton and Charles Conder. These young men set about establishing a distinctive school of national painting, portraying, in the words of Roberts, “a life different from any other country in the world”. Roberts’s A Break Away! (1891) is typical: a whirl of dust-bowl activity in which a skilful stockman on horseback struggles to contain his stampeding flock.

Streeton’s famous Golden Summer, Eaglemont (1889), the first painting by an Australian-born artist to hang in the Royal Academy, is a more gentle take on a pastoral theme. In these years, artists imagined Australia as a land of hardship but also beauty, blessed with gigantic gum trees and abundant sunlight.

During the 20th century, as the seedlings of Modernism flourished in the soil of Australian culture, the country’s artists imbued the landscape of their homeland with a sense of unsettling psychology. This is visible, for instance, in Albert Tucker’s oil-on-cardboard Sunbathers (1944), in which misshapen bodies on a beach look like pink-and-crimson shrimps griddled on some infernal barbeque beneath a glowering sky.

The painting feels like a riposte to Charles Meere’s Australian Beach Pattern (1940), which freeze-frames a crowd of pleasure-seekers in swimwear relaxing on a beach. There is something almost fascistic about their groomed appearances and taut, pumped-up physiques — they interact with all the spontaneity of a tightly orchestrated fashion shoot.

The best-known exponent, though, of this new strain of melancholy and unease was Nolan, who is represented here by several paintings from his famous series about Ned Kelly, in which the legendary bushranger appears in homemade armour — a Modernist black rectangle that looks like a fancy bottle opener. We also see Nolan’s Inland Australia (1950), a disturbing rocky vista that resembles nothing so much as flayed flesh, and Pretty Polly Mine (1948), a surreal picture in which a mine manager feeding birds in the desert while dressed absurdly in a suit is menaced by an oversized parrot tumbling out of the sky. The confident, pioneering spirit of the previous century has been replaced by something dark and strange — but the interaction of man and the Australian landscape is still very much to the fore.

At times, Australia feels more like a history lesson than an exhibition: we learn about important moments such as the gold rush of 1851 and the construction of Sydney Harbour Bridge, and discover as much about the country’s culture and customs as we do about its art. In a sense, this didacticism is appropriate, since several pictures, such as William Westall’s View of Cape Townsend and of the Islands in Shoal-Water Bay, Taken from Mount Westall, 1802 (c.1810), introduced British audiences to their Australian colony when they were first shown in London during the 19thcentury.

Often the art itself is far from amazing — indeed some of it feels downright feeble or derivative. But harping on about that would be churlish, especially at the end of an Ashes summer in which the Aussies were beaten yet again. Rather, think of this as the exhibition equivalent of a grand and informative television documentary series: detailed, comprehensive, omniscient, in places beautiful.