The Imperial War Museum is one of the most extraordinary museums in the world. Its contents and presentation triumph over the three words of its title, each usually causing dread rather than enthusiasm: imperial (discredited unless to do with Roman history); war (just horrible, and we shouldn’t do it); and museum (well, isn’t that mausoleum?) 

In fact, its collections embrace the modern world, and are perhaps the most insightful and visible tour of modern history that we have. 

The year 1915 was a big one for Kazimir Malevich, as it was for the course of modern art. It was the year the Black Square was first exhibited (June 1915 is the likeliest date of the painting’s execution, though Malevich himself dated it to 1913, insisting it derived from his designs for Futurist opera Victory Over the Sun). A simple black square on a white ground, it presented a gesture so bold, so audacious that it can only be rivalled by Duchamp’s Fountain of 1917.

Do we need more? Over the past 60 years thousands of books and bibliographies about Virginia Woolf (1882-1941) and the group of friends, lovers, spouses, partners, children, and houses with which she is associated, have been published, not to mention movies and plays and a more hidden mountain of academic dissertations. 

It’s 70 years since Mondrian died in New York, leaving unfinished his last painting, Victory Boogie-Woogie, an ebullient title quite at odds with the buttoned-up asceticism we normally associate with this artist. The Courtauld Gallery showed a small survey two years ago, which paired his flat grid compositions with the paintings and white reliefs of Ben Nicholson, focusing only on his two years in London (1938 to 1940).

Rimsky-Korsakov’s bizarre final fantasy, puffing up Pushkin's short verse-tale to unorthodox proportions, has done better in Britain than any of his other operatic fairy-tales. That probably has something to do with its appearance in Paris, six years after the composer’s death in 1908, courtesy of a brave new experiment marshalled by that chameleonic impresario Sergei Diaghilev.

When Ryan Gander’s wife wanted a designer lamp, the versatile artist knocked one up from junk. She was so impressed he sold it as an artwork and by now has made 55 in his garden shed. Three are here in Manchester, made from foil food trays, a guitar stand and concrete. These pieces are quite unrepresentative of the rest of this highly conceptual show, but in a diverse, major survey there appears to be no truly representative way in.

Digital Revolution begins with an archive section taking you back to the 1970s when Ralph Baer developed a video game allowing punters to play ping pong on TV (below right: poster for the original Pong arcade game) and Steve Jobs worked on Break Out, in which a virtual ball bounces off a bank of horizontal lines.

The National Gallery has a range of personas it adopts for its exhibitions, and for this one, about colour, it has deployed the po-faced, teachy one. The pompous tone is because it’s not just about art this time, there’s science in it, which makes it extra serious. And we know it’s science, because the posters and promotional material look like the cover of a chemistry textbook, with bursts of colour against a black background reminiscent of an explosion in a laboratory, or something exciting in space.

From Apocalypse Now to Blue Velvet to Speed, as a screen presence Dennis Hopper grew ever more scary. Lately gallery-goers have got to know another side of Hopper via his painting. Now there is a belated run-out for his work as a photographer, although work is maybe the wrong word. He spent much of the Sixties with a camera slung round his neck, but didn’t make a dime from any of his pictures. “They cost me money,” he said, “but kept me alive.” Hopper rode out of the decade on a Harley as director of Easy Rider and he didn’t pick up a camera again.

Bridget Riley’s mural for St Mary’s Hospital in Paddington, which was unveiled in April this year, is something I’ve seen only in photographs. And on seeing it for the first time my reaction, I’m afraid, was, “Oh no". It obviously didn’t help that the photographer had wildly exaggerated the one-point perspective, so that the parallel lines of two facing walls converging sharply made you feel the vertiginous pull of a rabbit hole.