My daughter has a book called Luna Loves Art. It’s a shameful thing — designed to appeal to the tastes and egos of parents rather than the imaginations of children. Luna visits a fictional gallery with various sculptures chosen, presumably, to paint modern art in its most primary colours. Among them, there’s a Jeff Koons balloon dog, a Henry Moore family group, a Yayoi Kusama yellow pumpkin, and a Louise Bourgeois spider.

These are works so famous that they’ve become a kind of shorthand for “art”. And when something is as familiar as that, it becomes almost impossible to look at. It’s why so many people’s first remark on seeing the Mona Lisa in the paint is that it’s a bit small. I was expecting a similar experience at the Hayward Gallery’s new Louise Bourgeois show: a bunch of big spiders that I’d seen before. But Bourgeois is a much more subtle and ambiguous artist.

Titled The Woven Child, the exhibition bills itself as a retrospective —  but it focuses on the last two decades of the artist’s life when she began working in textiles. It’s no less rich for it, but I did come away wanting to know much more about a woman who lived through the entire twentieth century — especially one whose work is so intimate and preoccupied with the past.

But weaving is also a quintessentially female activity

One of the first sculptures you encounter is Cell VII (1998), a kind of cupboard made from reclaimed doors containing a model of the artist’s childhood home, items of her mother’s clothing and — gratifyingly — a spider. Her mother was a weaver, and as a child in Paris in the 1920s, Bourgeois worked in the family business repairing tapestries. We’re told that for her, spiders are a symbol of the mother, and the intricate webs they weave from their own bodies a metaphor for the artistic process. But in Cell VII the spider also bespeaks dusty corners, memory and abandonment — themes that are found throughout the exhibition.

Many of the sculptures are roughly stitched, which gives them both a fragile impermanence and a palpable sense of the physical act of making them. Weaving is replete with classical allusion, from Penelope unpicking her embroidery to Arachne challenging Athena to a sewing competition. Bourgeois’s In Respite, from 1992, features black spools of thread which recall how the fates measure out mortal lives in lengths of yarn and determine the moment of death with a snip of their shears.

But weaving is also a quintessentially female activity, in contrast to the much more macho pastimes of hewing sculptures from stone or casting them in bronze. And female identity animates everything in this exhibition. Many of the works even take their names from archetypes like The Fallen Woman (1981) and The Good Mother (1991). 

Untitled, a work from 1996, comprises a metal structure on which diaphanous undergarments and a black sequined dress that had belonged to the artist hang from cow bones. The explanatory text quotes Bourgeois, “These garments have a history, they have touched my body and they hold memories of people and places. They are chapters from the story of my life’. For women, clothes are anything but superficial — you can imagine Bourgeois, then in her 80s, making this sculpture, and vividly, tactually, remembering how confident and beautiful she’d felt in that black dress. 

Another piece, Eugenie Grandet (2008), is made out of monogrammed linen handkerchiefs she’d had in her trousseau when she got married and moved to America in 1938. Both are reminders of how much of femininity consists of what we own, rather than what we do.

By concentrating on the later years of Bourgeois’s career, this exhibition celebrates an extraordinary final flourish. Like Matisse, who turned to paper cutouts when he could no longer paint, she was clearly an artist with a restless creativity that only died when she did in 2010. But the tight focus also obliterates so much of the context. This is a woman who studied with Fernand Leger, exhibited with the Abstract Expressionists, and campaigned to raise awareness of Aids. The works in this exhibition were made in the 90s and noughties, when the Young British Artists were in the ascendant, and you can see echoes of Tracey Emin, Sarah Lucas and even, in the use of vitrines, Damien Hirst. But the relationship between that thrusting new generation and an individual who bestrode so much that went before them goes unexplored.

Then again, curators and gallerists have to make choices. Odd then, that those behind a show dedicated to someone who deals so viscerally with womanhood decided to insert a coy little notice advising that one of the rooms contains “depictions of a sexual nature’. These turn out to be pairs of copulating, humanoid pillows with wooden limbs. The same sign tells viewers that there are images of “pregnancy’. I struggle to see how either requires caution. Surely, it is the idea that people need to be warned about images of pregnancy — which is both an everyday phenomenon and an integral part of human existence — that is offensive.

Aside from that, the curation in this show is unobtrusive, with wall text kept to a minimum. The same can’t be said of the catalogue essays, which contain such regrettable sentences as, “Hinting at a multidimensional topology of identity, this bodiless head manages to evince a polymorphous corporeality’. 

But we should forgive the Hayward’s Director, Ralph Rugoff, a few linguistic infelicities. Not just because he has assembled some 90 works, many of which have never been seen in public before, and each of which holds an uncanny fascination. But because Bourgeois’s work combines sensations, textures, techniques and fragments of ideas in a way that can only really be experienced visually. Which is, undoubtedly, reason enough to go and see this show.