To many people, the work of Dutch artist Maurits Cornelis Escher exists in that space reserved for jesters, gimmick merchants and easy-on-the-eye crowdpleasers.

Better known as MC Escher, his bold, illusionary, perspective-popping woodcuts and lithographs lend themselves to the sorts of posters you used to find in sixth form common rooms and student bedsits. Or on calendars. Or, as seen in a cabinet in the National Gallery of Scotland's terrific Escher retrospective, on record sleeves.

Under glass in the show's final exhibit are two such examples from 1969: Mott The Hoople's eponymous debut album, which uses Escher's 1943 work Reptiles, and L The P by The Scaffold, of Lily The Pink fame. It uses Escher's famous Ascending And Descending, a staircase in some imagined fortress which seems to be rising and falling at the same time. It's a dizzying thing to contemplate.

In common with JRR Tolkien, Escher was nonplussed and not a little irked by all this. He didn't like 1960s subculture co-opting his work and proved it by refusing a commission to design a sleeve for The Rolling Stones' Let It Bleed album.

But despite the considerable traction Escher had in late 20th-century popular culture, it's only a fragment of his story, a postscript to the very last stages of a long career. Track back through the preceding five decades, as this fine exhibition does, and you see that the breadth of his talent was as wide as the range of his interests.

Most notable of all, however, is how screamingly modern Escher seems. That notion begins with the two self-portraits hung in the entrance corridor, each showing the artist in his twenties with coiffed hair, full beard and luxurious moustache. There isn't a hipster hangout anywhere that doesn't have a barman sporting the same look - and probably with something Escher-like tattooed on his arms into the bargain. Perhaps Snakes, Escher's last work and a rare example of him using colour.

Other examples of Escher's modernity drop into your lap in every room. The way he takes from science, architecture and mathematics, for example. His geologist half-brother was an expert in crystals and he had friendships and correspondences with the mathematicians Roger Penrose and Harold Coxeter, and we can see those interests and connections in works like Mobius Strip II (Red Ants), from 1963, and the 1954 woodcut Tetrahedral Planetoid (Tetrahedral Planet). It shows an apparently symmetrical townscape of steps and towers, rendered as a solid with four triangular faces and superimposed onto what looks like an asteroid.

The way Escher takes from here, there and everywhere is also refreshingly modern, a cut-and-paste approach which pulls in influences from Surrealism, Cubism, Art Nouveau, the work of Hieronymous Bosch and his 15th-century contemporary Rogier van der Weyden, Japanese design and, perhaps most inspirational of all, Islamic art.

Escher twice visited the Alhambra, Grenada's jaw-dropping Moorish palace, and also made work in Cordoba's equally awesome Mezquita, and it isn't hard to see the connection between the interlocking and repeating designs of Islamic decoration and Escher's own geometrical investigations into tessellation and vanishing points.

The exhibition consists of around 100 works loaned by the Gemeentemuseum in The Hague and is presented chronologically. It begins with one of Escher's earliest woodcuts (an image of a cat, from 1919) and runs through the architecturally precise townscapes he executed on several trips to Italy. He later lived in Rome, where he had his first solo exhibition, but he left as Mussolini and Italy became increasingly bellicose. From Rome he moved first to Switzerland and then Belgium before returning home to settle in Baarn in Holland during the Second World War. It was a difficult period, made worse when his mentor and former teacher, the Jewish artist Samuel Jessurun de Mesquita, was arrested and sent to Auschwitz where he and his wife were gassed. Three months after his death, Escher made a bleak lithograph called Encounter, one of the few works in which the stridently apolitical artist seems to comment implicitly on the turmoil surrounding him. It has a harrowing feel.

Elsewhere Escher prefers to show reality as it isn't rather than as it is, or simply abstracts his political or social concerns by polarising them into concepts of order and chaos. We see this best in Contrast (Order And Chaos) which shows something called a stellated dodecahedron merged with a glass sphere but surrounded with what look like the contents of his rubbish bin.

After the war Escher stayed in Baarn in Holland and many of the rest of the works in the show's final room were made there. One of the exceptions is the exhibition's largest work, Metamorphosis II, begun in 1939 and finished in 1940.

A shade under four metres in length it was made using 20 woodblocks and, reading from left to right, it starts with text blocks which give on to graphic black and white squares. These in turn become tessellated reptiles, then larvae-containing hexagons which hatch into bees which become fish which become birds. The whole thing ends in a townscape which becomes a chessboard and it ends with the same word it started with: Metamorphose. Like everything else in this smartly presented retrospective - amazingly the first such exhibition of Escher's work in Britain - it's utterly absorbing and as exquisitely rendered as anything by the Renaissance masters. A real treat.

The Amazing World Of MC Escher is at the Scottish National Gallery of Modern Art's Modern Two until September 27