The palace itself is older than the artist. Built in 1760 by Pieter de Swart, it passed through colonial heirs and Napoleonic guests and Hope bankers before Queen Emma bought it in 1896 and made it her winter home. After Emma died in 1934, the building served as a working office for the next three Dutch queens - Wilhelmina, Juliana, and Beatrix - until Beatrix moved her office out in 1984. In 1991, by then a private citizen, Princess Juliana sold the building to the city of The Hague on condition that it would only be used for cultural purposes. The Kunstmuseum Den Haag held travelling exhibitions in it for a decade - Rodin, Venetian glass, Frida Kahlo - and then, in November 2002, the building took on its permanent identity: a museum dedicated to one of the most popular Dutch artists of the 20th century, M.C. Escher.

The collection runs from Escher's early Italian landscape woodcuts of the 1920s and 1930s - quiet, atmospheric, mostly unfamous - through the mirror prints, the tessellations of interlocking lizards and birds and fish, and into the late, impossible work that made him a global household name. Sky and Water, with birds at the top morphing into fish at the bottom through a middle band where each is the negative space of the other. Belvedere, a building whose pillars meet floors they cannot possibly meet. Waterfall, where water runs downhill in a perfect loop and arrives back at the top of itself. Drawing Hands, the print most often used to illustrate the philosophical idea of self-reference: a right hand drawing a left hand that is drawing the right hand. The museum holds all three known versions of Metamorphosis - small early sketches, the second print, and the third version, seven metres long, displayed in a circle so that the figure transforms continuously into itself and back again. Standing inside that circle is the closest most people get to walking inside an Escher.

The Rotterdam artist Hans van Bentem made fifteen chandeliers for the museum, custom-designed for the palace and for the work it now houses. There are conventional crystal pieces. There is also a chandelier in the shape of a shark. A skull. Spiders. A sea horse. In the ballroom, a star chandelier hangs between two mirrors and reflects to infinity in both directions - an Escher print rendered in glass and chain rather than ink on paper. The parquet floor was designed in 1991-92 by the American minimalist Donald Judd, who applied his familiar logic of coloured geometric panels to the timber surface underfoot. Visitors looking up at the chandeliers, down at the Judd floor, and forward at the prints on the walls are surrounded on all sides by people having a quiet joke at the expense of regular space.

The third floor is dedicated to optical illusion. The signature attraction is the Escher Room - a real, three-dimensional space built on the principle that Escher exploited in his drawing: a room with a sloping floor and walls of unequal heights, painted with perspective cues to flatten in the eye. Stand in one corner and you tower over the room. Walk across to the other corner and you shrink. Children become taller than their parents. Parents shrink below their children. The trick has been known since the Renaissance and has appeared in many science museums, but inside this particular palace, three rooms away from a Belvedere print, the joke lands differently. The illusion that has been a graphic effect on paper becomes something the visitor can step into.

In 2015 a Dutch expert in print authentication, Sasja Susan, told the press that many of the prints on display were not original Escher impressions at all but high-quality replicas - scanned from genuine prints, printed on the same paper Escher used, displayed beside labels that did not always make the distinction clear. The story landed badly. The museum's response was, in essence, that originals are fragile, that exhibition conditions damage paper, and that high-quality facsimiles let many more people see the work at all. Both arguments have merit. The controversy briefly threatened the museum's reputation; the visitor numbers, after a wobble, recovered. The Escher industry - posters, T-shirts, computer-generated tessellations, mathematical papers, the continued reprinting and reframing of the work - turns out to depend less on the physical authenticity of any particular print than on the persistent power of the images themselves. Stand in front of Drawing Hands. Whether the paper is from 1948 or from 2005, the hand is still drawing the hand that is drawing it - and the trick still works.