The exhibitions you must see this August

One of the earliest civilisations, Peru can boast the longest continuous history of textile production in the world. This exhibition brings that extraordinarily vibrant heritage to the UK, from centuries-old costume, including a rare pre-Hispanic tunic made from macaw feathers, to the work of contemporary Peruvian designers such as Meche Correa and Chiara Macchiavello. Peruvian design continues to have international reach, from an unusual 9th-century weaving technique that was a clear influence on the work of celebrated textile artist Anni Albers to the costume of the Ashaninka tribe, which inspired a 2014 collection by fashion designer Vivienne Westwood.

Follow the life journey of Julie Cope, Grayson Perry’s fictional everywoman, in this first solo exhibition of Perry's work in Scotland. The four large-scale tapestries are accompanied by a narrative voiced by Perry himself. Originally created for A House of Essex, a secular chapel dedicated to Grayson’s home county and Julie Cope’s story, they explore contemporary questions of class within an artform largely associated with privilege and heritage. The exhibition also reveals the variety of crafts and skills that went into making the tapestries, and explores both hand and machine-weaving.

At 32, Natalia Goncharova had established herself as the leading figure of Russia’s avant-garde and went on to be celebrated internationally as an artist who transcended 20th-century art movements. A quick glance at her output and you can see why – futurist body art, religious works, nude paintings (resulting in an obscenity trial), significant contributions to fashion and interior design, and a career-long collaboration with the Ballets Russes. This exhibition is the first ever retrospective in the UK of this trailblazing artist and includes works never displayed here or loaned before.

Feeling fraught about modern Britain? Take heart – you’re in excellent company. This exhibition looks at the role of art in the time of Brexit, but also examines the fears and dreams of our immediate artistic forebears through a rich showcase of British art from the last century. Paintings, sculpture, photography, film and more by artists including David Hockney, Bridget Riley, Henry Moore, Henri Gaudier-Brzeska and Victoria Sin explore questions of identity and belonging – and remind us that our urgent contemporary concerns find an echo in the challenges of the past. And if you have a National Art Pass, you can enjoy 20% off in the café and shop as further consolation.

Celebrate the 50th anniversary of NASA’s Apollo 11 mission, which landed the first humans on the moon, in the UK’s biggest exhibition dedicated to all things lunar. From a Mesopotamian tablet showing how lunar eclipses were considered bad omens, to the ‘Snoopy Cap’ Communications Carrier worn by ‘Buzz’ Aldrin during the first moon landing, 180 objects explore the cultural and scientific story of our relationship with the moon over time and across civilisations. Other highlights include a rare lunar meteorite and the earliest known drawing of the moon’s surface made from telescopic observations in 1609.

When Mount Vesuvius erupted and blotted out Pompeii, it brought an end to a town of insatiable foodies. A thriving exporter of wine, olives and fish sauce throughout the Mediterranean, Pompeii was typically Roman in its enthusiasm for the culinary traditions of other peoples – and its passion for gourmet goods is evident in everything from the frescoes that were found in wealthy villas to the remains recovered from kitchen drains. This exhibition brings Pompeii's passion for food and excess to life, and features objects that have never before left Italy – including luxury dining-room items and carbonised food which was left on the tables during the eruption.

This is a unique opportunity to get inside the mind of Leonardo da Vinci through notes and drawings from three of his notebooks. On the 500th anniversary of his death, it’s still possible to witness the artist’s and scientist’s creativity at work on what he believed to be the ‘cause of all life’ – motion. From the movement of the human body and flow of water to astronomy and mechanics, his meticulous notes and sketches are the foundation of his inventions and illuminate the mastery of his paintings. It’s also the first time the Codex Leicester – one of his most important scientific notebooks – can be seen in the UK since Bill Gates purchased it for a record sum in 1994.

If you’re based in northwest England, this is a rare opportunity to see a substantial collection of works by leading American pop artist Roy Lichtenstein close to home. Lichtenstein was a pioneer of the new art movement alongside artists such as Andy Warhol, Jasper Johns and James Rosenquist. Responding to and mimicking popular mass culture of the 1960s, his bold graphic style and signature hand-painted dots, which recall the aesthetics of comic books and commercial newsprint, are still immediately recognisable today. Visitors with a National Art Pass can then treat themselves to a memento from the shop while enjoying 10% off.