Near the beginning of Riot Days, Maria Alyokhina – a member of the Russian performance art collective Pussy Riot – recalls how, during her schooldays, she would surreptitiously practise drawing graffiti at the back of her school notepad. As term progressed, the sketches would grow from the back at a similar rate as the official schoolwork did from the front, until suddenly, the two would “meet in the middle. And, next to your history notes, graffiti appears. Which turns history into a different story.”

In March 2012, Alyokhina and two other members of Pussy Riot – Nadezhda (“Nadya”) Tolokonnikova and Yekaterina (“Kat”) Samutsevich – were arrested and later charged with “disorderly conduct, committed with the purpose of inciting religious hatred by a group of persons in an intentional conspiracy”. Pussy Riot had been formed as a woman-only group after the male members of their earlier art collective Voina (“War”) had refused to take part in a guerrilla action, Buss the Buzz. In that action, actors had approached police officers, asked for directions, and responded with grateful effusions culminating in kisses on the lips. But the men had refused to kiss male officers; Voina had fizzled out; and a couple of years later Pussy Riot was formed instead as a specifically feminist retort to patriarchal power in Russia.

In February 2012 – in the midst of the “snow revolution” against electoral fraud in Russia, and before the re-election of Vladimir Putin in the 4 March elections – six members of Pussy Riot planned an “action” in Moscow’s Cathedral of Christ the Saviour. Having smuggled a guitar and amplifier into the cathedral, Alyokhina, Tolokonnikova, Samutsevich and two other women donned dresses, tights and balaclavas in acid tints, clambered on to a platform by the altar, and belted out lines including “Virgin Mary, Mother of God, chase Putin out”, “Shit, shit, holy shit!”, and “Virgin Mary, Mother of God, become a feminist”.

Initially, Pussy Riot seem to have been rather deflated by their performance, which had been recorded by videographers for dissemination across the internet. It had resulted in very little usable footage, which had to be spliced with material filmed earlier, in a less fraught location, to create a transmissible video. But as it became clear that Alyokhina, Tolokonnikova and Samutsevich were going to be arrested, the world’s media became hooked by their open defiance of Putin’s attempts to curtail freedom of speech. In hiding, the trio found themselves conducting Skype interviews from Moscow cafe toilets with al-Jazeera journalists, before being located and detained by the police. On 17 August, they were found guilty and sentenced to two years in Russian prison colonies.

Riot Days is Alyokhina’s account of that performance, trial, incarceration and her subsequent protests in prison – including hunger strikes – against human rights abuses there. The book enacts the graffitied history notes of her schooldays, the clash of official and unofficial forms of expression, of authority and protest. She parcels out the period between 2011 and her release from prison in December 2013 in textual fragments, fleeting tableaux which mark time like the “shutter clicks”, clock ticks and door slams that form her auditory experience of the Russian prison system. In Riot Days, official pieces of historical evidence – such as news reports of Pussy Riot’s action, citations from speeches by Putin and the Russian Orthodox bishop Patriarch Kirill, and excerpts from the trial transcripts – come up against a punk version of history, a range of dissenting references and citations from Alyokhina’s key aesthetic and political influences.

A mantra recited throughout the book – “to back down an inch is to give up a mile” – echoes a screen-printed poster produced by the Atelier Populaire, a collective during the 1968 student/worker uprising in Paris, warning that “céder un peu, c’est capituler beaucoup” (to give in a little is to capitulate a lot). Alyokhina scrawls the motto on “the first T-shirt I’d created myself”. The figures and publications invoked by Alyokhina as part of her alternative history, a history of Russian protest rather than power, include the avant-garde artist Alexander Vvedensky; the poet Osip Mandelstam; the journalist Alexander Podrabinek; the Soviet dissident periodical Chronicle of Current Events; Varlam Shalamov’s The Kolyma Tales, his short stories of labour camp life; and the underground feminist punk movement Riot grrrl. The textual tapestry is punctuated by literal graffiti, too: Alyokhina’s own doodles of the symbols of power and rebellion – the clenched fist accompanying “No Pasarán!” (They shall not pass) – as well as apparently more innocuous images, such as “icy giraffes”.

From left: Yekaterina Samutsevich, Alyokhina and Nadezhda Tolokonnikova in court in Moscow, in October 2012. Photograph: Natalia Kolesnikova/AFP/Getty Images

Particularly resonant for Alyokhina is the work of Alexander Brener, a performance artist who, in 1997, was jailed for painting a green dollar sign on an abstract painting of a cross by the avant-garde suprematist artist Kazimir Malevich. Brener justified his action by emphasising how the “cross is a symbol of suffering, the dollar sign a symbol of trade and merchandise”. The graffitiing of the dollar over the cross was intended, he explained, to begin a dialogue with (the deceased) Malevich about corruption in the commercial art world.

Like Brener, Alyokhina expresses profound concern about corruption and commodification in Russia, especially of religion. A member of the Orthodox church herself, she was appalled at the charge levelled against her by prosecutors, that calling on the Virgin Mary to “become a feminist” and “chase Putin out” was intended as a smear. For Alyokhina, feminism is a means to purify Russian religion and politics of patriarchal corruption. The cathedral that Pussy Riot was accused of defaming was itself tainted by corruption, she points out: “Government officials and other higher-ups” were able to bypass queues to view a sacred relic. And the church was profiting from hosting corporate events and flogging “fine porcelain eggs and custom-made replicas of imperial medals … for 500 bucks” in its gift shop.

Pussy Riot’s performance, in which Alyokhina dressed in green tights in a cathedral which is notably green inside, with a “green carpet” leading to the altar, guarded by a keeper dressed in a green uniform, might be read as a means of reproducing Brener’s graffitiing of the green dollar on the cross in Malevich’s painting. She’s certainly not shy about positioning herself and the band in this broader tradition of art and dissent: “There were eight of us, like the eight dissidents in 1968,” she emphasises.

This litany of avant-garde aesthetic influences might suggest Riot Days is forbiddingly erudite, and the book does not disguise its allusiveness. But this is no postmodern defence of moral relativism: all told, it’s a pacy page-turner. In her account of “the passion of Pussy Riot”, Words Will Break Cement, the Russian-American journalist Masha Gessen perceptively notes the faint embarrassment experienced by Tolokonnikova and Alyokhina – both steeped in “theory” from precociously young ages – when talking about the concept of “the truth”. But in the face of the lies and suppressions of Putin’s Russia, truth and honesty are precious concepts, and ones that Alyokhina defends in her life and in her book.

The fragments of text and art are arranged in a consciously orderly, chronological fashion, with subheadings that look both forward and back, unified by recurring imagery (for example, of the snow of the snow revolution) and by Alyokhina’s unwavering, invigorating voice. “I have to remember things in the proper order,” she writes: “I need order.” In a world in which words “are being used to mean their opposites” (as Tolokonnikova described to Gessen) – a world in which it is Pussy Riot and not Putin who are held responsible for engendering “disorder” – Alyokhina clings to order and the possibility of truth; or, at the very least, to the necessity for the rebuttal of lies. Resistance to lies is how freedom is forged, she reminds us, and surprise is the only appropriate response to mendacity: “If you stop being surprised by such things, you’ll be turning your backside to them and bending over for the rest of your life.”

Protest must be surprising, Alyokhina emphasises. Riot Days could so easily have been a straightforward, from-the-horse’s-mouth confessional account of one of the most publicised political protests of recent years. Alyokhina takes on a far greater challenge: creating a text that is not just a reflection on a piece of art, but becomes one itself, and one that, in many places, lives up to her own criteria of protest: that it must be “desperate, sudden, and joyous”.

• Rachel Hewitt’s A Revolution of Feeling will be published by Granta in October. To order Riot Days for £14.44 (RRP £16.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.