The Icelander’s first major UK retrospective at the Barbican contains works to split your sides – and others to break your heart. Of the former, the highlights are his performance as a ludicrous Grim Reaper unmasked by a group of schoolkids and a  video sequence of his mother repeatedly spitting at him. Of the latter, The Visitors is not only tragically beautiful but is also one of the finest works of art this century. It features Kjartansson and eight compatriots singing and playing his ex-wife’s emotion-soaked lament for their failed marriage . Each performer appears on a separate screen while we, the audience, stand or sit surrounded by nine different images that engulf us in gorgeous, hypnotic yet soul-searing music for 64 exquisite minutes. I was so overwhelmed I watched it twice – though a veil of my own tears. Astounding and unmissable.

An amazing evening at Laban theatre in Greenwich as the acclaimed choreographer gave us a lesson in social anthropology – and so much more. InNoForm opened with six bare-backed dancers squirming and thrashing in pools of dirty white light like protozoa writhing in the primordial ooze. We were, I felt, witnessing nothing less than the emergence of life on earth. What followed seemed to be the Darwinian evolution of man from ape to autocratic homo sapiens and was brilliantly captured with staccato movements perfectly performed. If the political message seemed blurred by the artistry, the second half of the show went for politics in the raw, with music giving way to hustings oratory and racist chants – but always illustrated with wonderful choreography. There were witty references to Theresa May and Brexit but on the whole the mood became ever darker, eventually erupting into violence as five of the dancers began making monkey noises and throwing bananas at the sixth. All the performers were black, which made it deeply uncomfortable to watch. Finally the troupe spilled into the audience and we found ourselves face-to-face with the hatred that pervades all extremism. It was an astonishing end to an astonishing event that was challenging and exhilarating in equal measure. No wonder it got a standing ovation.

This important retrospective at Tate Modern contains some surprising disappointments such as her iconic but in reality rather flat New Mexico landscapes. It also contains any number of wonderful moments – the justly famous flowers and skulls and, best of all, her abstractions. I especially loved Blue And Green Music. The show includes a brilliant array  of contemporary photographs of her including an Ansel Adams portrait of her and desert guide Orville Cox which is so fabulous it almost steals the show. Once you’ve seen all the pictures, walk across to the Switch House and take a look in the Louise Bourgeois room where a comparatively small version of Maman – truly iconic – and the extraordinary exploration of infinity titled Cell (Eyes And Mirrors) reveals that though a key modernist pioneer, O’Keeffe is a long way from being the 20th century’s greatest woman artist. Speaking of comparisons, the O’Keeffe exhibition includes four paintings of cottonwood trees from the decade after the Second World War. They are marvellous – but not as marvellous as a pen-and-ink drawing of a solitary tree in winter created nearly 500 years earlier by Fra Bartolommeo which is the highlight of a small but perfectly formed display of tree art at the Courtauld gallery.

Still at the Courtauld, nine works inspired by the seasons by this great American have been given to the gallery – and are a must-see for anyone with even a passing interest in modern art. The remarkable series offers a sort of traditional take on the seasons themselves (wintry snow, golden autumns, summer greenery, burgeoning spring) but sprinkles them with symbols of creativity, autobiography, art history and the relentless passage of time. A fascinating exhibition and a welcome addition to the Courtauld’s wonderful collection.

I’d just got used to the idea that Swedish mystic Hilma af Klint had pioneered abstract art years before Kandinsky, Mondrian and Malevich when I found out Georgiana Houghton, a Victorian English medium, got there first by several decades with a series of bizarre but beautiful “spirit” paintings. She claimed her hand was guided by great artists from history and even by St Luke. But even if you laugh off the idea, there’s no doubting the astonishing originality of these pieces, which tremble and shimmer with colourful swirls and lines and pious symbols. Barmy? Possibly. But it’s worth remembering af Klint, Kandinsky, Mondrian and Malevich were all followers of another odd cult, Theosophy. Check out Houghton’s works at the incomparable Courtauld Gallery till September 11.

The London Oriana Choir launched a three-year residency at the Royal Museums Greenwich with a glorious concert of works composed by women – including the world premiere of Cheryl Francis-Hoad’s setting of the Shakespearean sonnet So True A Fool Is Love. This brilliant new piece features an extraordinary sequence in which sections of the 70-strong choir counterpoint one another in differing tick-tock rhythms. Other highlights of the concert – in the amazing space beneath the copper-bottomed hull of the Cutty Sark – included 1,000-year-old tunes from Germany and Bulgaria, Judith Weir’s Drop Down, Ye Heavens, From Above, the stunning O Oriens by Cecilia McDowell and Kerry Andrew’s gorgeous O Nata Lux. The choir – conducted by Dominic Peckham – the composers, their creations and the unique setting combined to make this one of the year’s most memorable events so far.