It is a commonplace to describe Leonardo as an enigma whose genius, and perhaps even something of his character, is revealed through his works. But as his works survive only in incomplete and fragmented form, it is drawing, the practice common to all his various endeavours, that brings coherence and perhaps even a comprehensive view of a lifetime’s labours.

There are children screaming in a nearby playground. Their voices rise and fall, swell and drop. Interspersed silences fill with the sound of running, the movement and cacophony orchestrated by a boy who leads on the catch tone. It's simultaneously otherworldly and juvenile, adept and improvised – a fitting soundtrack to Anish Kapoor's latest exhibition at Lisson Gallery. 

Dried flowers like offerings lie atop a gauze-covered rectangular frame. Pebbles surround its base alongside plaster casts, a desiccated dragonfly and an animal foot charm. Their placement is purposeful; their exact significance unclear. Four rib-high figures with moon faces, sausage string necks and wafer-thin bodies face the frame. Three wear golden gowns like devotees or disciples; all bear pendulous, darkly bellying stomachs before them over their clothes.

Mike Nelson has turned the Duveen Galleries into a museum commemorating Britain’s industrial past (pictured below right). Scruffy workbenches, dilapidated metal cabinets and stacks of old drawers are pressed into service as plinths for the display of heavy duty machines. Rusting engines, enormous drills, knitting machines, crane buckets, a concrete mixer, a paint sprayer and various other unnameable objects are thereby elevated to the status of sculptures.

Tate Modern’s retrospective of Dorothea Tanning is a revelation. Here the American artist is known as a latter day Surrealist, but as the show demonstrates, this is only part of the story. Tanning’s career spanned an impressive 70 years – she died in 2012 aged 101 – but as so often happens, she was eclipsed by her famous husband, German Surrealist Max Ernst. 

Franz West must have been a right pain in the arse. He left school at 16, went travelling, got hooked on hard drugs which he later replaced with heavy drinking, got into endless arguments and fights, was obsessed with sex and, above all, wanted to be an artist but hadn’t been to art school. His life reads like a bad novel or Hollywood’s idea of the tortured genius struggling to make his mark in a world indifferent to his talents.

It doesn’t get better than this! Phyllida Barlow has transformed the Royal Academy’s Gabrielle Jungels-Winkler Galleries into a euphoric delight. Entering the space, you have to turn right and process through the three galleries; but by closing the end door to create the cul-de-sac of the title, Barlow has turned this somewhat prescriptive lay-out into a theatrical experience.

For an artist whose cerebral and frequently playful works reference physics, myth and music, Fausto Melotti’s artistic education was appropriately heterogeneous.

A whiff of chlorine hits you as you open the door of the Whitechapel Gallery. Its the smell of public baths, and inside is a derelict swimming pool with nothing in it but dead leaves and piles of brick dust. Damp walls, peeling paint and cracked tiles make this a sorry sight. The door to the changing rooms has been sealed shut and some joker has sawn through the wall bars.