Once upon a time, in the middle decades of the war-torn 20th century, there lived an Australian-born British theosophist and mystic, a respectable English woman hiding behind a man’s name, a gay and depressive Finnish Swede who lived half her life on a tiny island, and the firebrand daughter of a respectable Swedish farmer. These four women radically changed the landscape of children’s literature, making it wilder, stranger, more anarchic, and, crucially, more centred in the dreamy and unfettered imagination of the child.

PL Travers created Mary Poppins, whose sour magic Disney tried to tame. Richmal Crompton unleashed irrepressible Just William on to an unsuspecting conformist society. Tove Jansson beautifully gave us the mysterious outsider’s world of the Moomins. And from Astrid Lindgren bounded fabulous Pippi Longstocking, the strongest girl in the world with her carrot-coloured pigtails and her freckles, her pet monkey, her mismatched stockings, her good-humoured disregard of authority, her spirit of misrule and joy. Her roots were in the war (the first book, Pippi Longstocking, was published in 1945) and a decade of fear, but Pippi was a cheerfully outspoken, brave-hearted pacifist who protected the weak and stood her ground against bullies.

Her soil was a country of deep conformity and regulation, but she had a glorious disregard for dull bureaucracy and decorum. Hers was a world turned upside down: she slept with her feet on her pillows, blew her nose on her clothes, danced on the church pews, mocked the stiff and dreary grownup ways of being. She (literally) played with fire and she exploded into the world like a glorious catherine wheel. Some adults were shocked at her transgressive impudence, calling her depraved, dangerous, mentally ill, psychotic. But children loved her because she was theirs, on their side, an adult-free zone and a path to freedom. And all over the world, generation after generation, they still love her.

Lindgren was born in 1907; she died in 2002, aged 94. She lived the 20th century – and what a life it was, what a journey she made from a farmer’s daughter in rural south Sweden to single mother, internationally bestselling author, political activist, environmentalist, feminist, astute businesswoman, humanist, global brand, member of the establishment and fighter against it, whose funeral (on International Women’s Day) was attended by the Swedish royal family, the country’s prime minister and thousands of Swedes who lined the streets to say goodbye.

As a girl, she worked every day on the farm. She was a clever student who loved books and jazz and dancing, nature and adventure. She fizzed with energy – one friend talks of “sparks coming off her”. In defiance of the times, she wore slacks and jackets and her blond hair was cut à la garçonne (a photo of her at 16 shows her and her friends cross-dressing, scandalising the small town she came from). She left school early to work for a local newspaper. By 17, she was pregnant by the paper’s 50-year-old, married proprietor. By 18, she was a single mother working as a stenographer in Stockholm, though her son, Lars, lived with a foster family in Copenhagen for three years before his mother could reclaim him.

These hard years in Stockholm (her “promenade through hell”) are in many ways the heart of Jens Andersen’s fine and thoughtful biography, and the source of Lindgren’s writing life. Lindgren’s exile from her childhood home, her grim struggle with Lars’s coercive father, her determination to remain independent of him, the secret birth, her head-over-heels love for her little son, her long and anguished separation from him (though she went to visit as often as she could scrape together the money), her enduring guilt at not being with him and then her guilt at plucking him from the only family he had ever known – all these things find their way into her writing. As Andersen comments, her stories are full of parentless children, of abandoned boys and girls. Under the exuberance lies a darker story of loneliness and loss.

In 1931, she married her employer, Sture Lindgren, and was able to bring Lars home at last; three years later, she had a daughter, Karin. Now they were a neat, nuclear, prosperous Swedish family. During the war, she worked as a mail inspector for Swedish Intelligence (a self-titled “dirty” job) and at night her stories of Pippi’s exploits were told to her children. In 1945 she found a publisher. Her editor, Elsa Olenius, just happened to be a judge in the prestigious literary prize that her new author went on to win. (Lindgren had many strong female friendships and Andersen’s book is full of powerful, independent women.) Lindgren rocketed to fame and to fortune. She sold in Sweden, then Denmark, then all over the world. She got a part-time job as an editor (later, she was actually her own editor). She wrote dozens of books. She wrote TV scripts. She wrote diaries. She wrote thousands of long and attentive letters to readers. She took part in TV and radio shows, quick-witted and unafraid. She travelled all over the world, giving talks, signing books, accepting prizes. She was elected to De Nio (the Nine), a prestigious literary academy promoting literature, peace and women’s rights. She campaigned (very effectively) in multiple causes: against seal hunting, against a sclerotic tax system that meant one year her income tax bill was 102%, against house shortages, library closures, racism, child pornography… She earned a lot of money and then gave a lot away. She had a finger in every pie.

She survived (but never recovered from) the death of Lars in 1986, the death of her husband, the death of her siblings, her friends, of her first generation of readers. But new readers came and still they come. Although Lindgren was a media-savvy and shrewd businesswoman, organised, dynamic and phenomenally energetic, part of her was always Pippi: the rule-flouter, the freedom lover, steadfastly opposed to all demagoguery and hypocrisy, who at 70 was still climbing trees and who refused, in the face of her fear, to be afraid, and insisted, in the face of her depression, on joy. And Pippi was a loner, someone who had learned to rely only on herself, and to stand on her own ground. The last sight the reader has of her in the final Pippi Longstocking story, she is sitting alone, pensive, before leaning forward to blow out the candle and disappear into the darkness.

• Astrid Lindgren: The Woman Behind Pippi Longstocking by Jens Andersen is published by Yale University Press (£25). To order a copy for £21.25 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99