Friedrich Nietzsche, Karl Marx and Charles Darwin are the great triumvirate of 19th-century thinkers whose ideas still have huge impact today. Nietzsche was philosophy’s supreme iconoclast; his sayings include “God is dead” and “There are no facts, only interpretations”. Highly relevant, yet his association with concepts such as the Übermensch, master morality, slave morality and, possibly most dangerous, the will to power, have also contributed to him being widely misinterpreted. There are three myths in particular that need dynamiting: that his politics were on the far right, he was a misogynist and he lacked a sense of humour.

Misappropriation has been rife. Richard Spencer, a leader of America’s “alt-right”, claims to have been “red-pilled by Nietzsche”, while Jordan Peterson quotes extensively from him. But let’s start with the Nazis. Growing up in Bismarck’s reich, there were three things Nietzsche hated: the big state, nationalism and antisemitism. “Deutschland, Deutschland über alles, that is the end of German philosophy,” he wrote, and “I will have all antisemites shot.”

His sister Elisabeth held contrasting views. She married a notorious antisemite agitator (Nietzsche refused to go to the wedding), and the couple went off to Paraguay to found a New Germany of “pure-blooded” Aryan colonists. By the time the colony failed in 1889, Nietzsche had lost his reason. Elisabeth returned to Germany, where she took charge of her brother, gathered up all his papers and founded the Nietzsche Archive.

‘Is man God’s mistake, or is God man’s mistake?’ Photograph: Culture Club/Getty Images

When it came to faking news, Elisabeth was a pioneer. On her brother’s death in 1900, Elisabeth didn’t think his death mask was sufficiently impressive, so she faked a second one. She did the same to his writing, rummaging about in his literary estate, cutting and pasting at will. She published an unreliable biography of him and delayed publication of his autobiography, Ecce Homo, until she had deleted uncomplimentary references to herself.

Nietzsche was always very sparing in what he published, but he loved playing around with book titles. He wrote many more titles than books. One he scrapped was The Will to Power. He scrawled a shopping list on the abandoned title page. But Elisabeth took fragments from here and there, concocted a book called The Will to Power and published it under her brother’s name. It was such a success that a few years later she published a greatly expanded edition.

Elisabeth lived until 1935. This gave her almost 40 years to doctor texts and letters and manipulate the literary estate. The Nietzsche Archive became an institution filled with extreme rightwingers, whose aggressive nationalism chimed with her own.Among them were Oswald Spengler, and Alfred Bäumler, who oversaw book burning in Berlin and prepared Nietzsche’s texts for new editions, including another The Will to Power that again gave the impression the text had been authored by Nietzsche himself. Bäumler was joined as editor in the Nietzsche Archive by Martin Heidegger. The two of them took the extraordinary view that Nietzsche’s published works hardly counted because the real philosophy resided in the Nachlass, the unpublished literary estate that Elisabeth had already manipulated to her own ends. This allowed them to continue jigsawing dislocated fragments to put their own ideas into Nietzsche’s mouth.

Elisabeth greatly admired Mussolini. In 1932 she persuaded the Weimar National theatre to put on a play written by him. Hitler showed up during the performance and presented her with a huge bouquet of flowers. A year later, now chancellor of Germany, he visited the Nietzsche Archive, carrying his customary whip. He remained for an hour and a half. When he emerged the whip had gone. In its place he grasped Nietzsche’s walking stick, presented to him by Elisabeth.

'The gentlest, most reasonable man may, if he wears a large moustache, sit as it were in its shade and feel safe'

Hitler was infatuated with the idea of himself as the philosopher leader. It is impossible to prove whether he studied Nietzsche; it is widely believed he did not. The surviving books from his library during his time in prison in 1924, when he wrote Mein Kampf, do not include any works by Nietzsche. It must be possible they were part of his book collection at the time and have since been lost but his later library preserves no well-thumbed copies. The notorious film of the 1934 Nuremberg rally was given the deliberately Nietzschean title Triumph of the Will, but when the director, Leni Riefenstahl, asked Hitler whether he liked to read Nietzsche, he answered: “No, I can’t really do much with Nietzsche … he is not my guide.”

The complicated ideas contained in the books were of no use to him, but catch phrases such as “the blond beast”, the Übermensch (neither of which is a racial concept) and “beyond good and evil” could be put to infinite misuse. Yet even as Nazi propagandists and phrasemongers usurped Nietzsche’s words and meaning, some among them realised the absurdity. Ernst Krieck, a prominent Nazi ideologue, sarcastically remarked that apart from the fact that Nietzsche was not a socialist, not a nationalist and opposed to racial thinking, he might have been a leading National Socialist thinker.

Nietzsche also has an undeserved reputation as a misogynist. Born in 1844, he attended one of the best schools in Europe while Elisabeth was sent to Fräulein Paraski’s institution to be taught how to capture a husband, run a household and speak just sufficient French to be considered elegant but not (God forbid) learned. Yet Nietzsche treated Elisabeth as an equal. He gave her reading lists, urged her to think for herself and widen her knowledge by attending public lectures.

Leni Riefenstahl directs her crew filming of Triumph of the Will at Nuremberg in 1934. Photograph: Friedrich Rohrmann/EPA

In 1874, when he was professor of philology at Basel University, a vote was taken on the admission of women to the university. Nietzsche was one of only four who voted in favour, and the motion was lost.

In 1876, he travelled to Italy to join Malwida von Meysenbug, a feminist who campaigned vigorously for the emancipation of women. Meysenbug had been exiled from Germany for smuggling letters during the revolution of 1848, after which she settled among the political exiles in north London, working as a tutor. Malwida’s reputation was such that when Garibaldi sailed up the Thames in 1864, he summoned her to talk politics over breakfast on his yacht. Malwida was starstruck by Garibaldi’s Pirates of the Caribbean glamour as he lowered an upholstered armchair to winch her comfortably up onto the deck for their breakfast meeting.

Nietzsche and Meysenbug intended to found a school for free spirits in the caves beneath Sorrento.The free spirits were to include women and nothing would be off limits in their study of culture, philosophy, aesthetics, religious scepticism and sexual freedom. The school never materialised but his friendship with Meysenbug widened Nietzsche’s feminist circle to include Meta von Salis-Marschlins, an activist for women’s suffrage, and Resa von Schirnhofer.

By the 1880s, women were allowed into the university lecture theatre as Hörerin, “listeners”. Nietzsche encouraged his sister, Salis-Marschlins and Schirnhofer to apply. In 1887, Salis-Marschlins became the first woman to gain a PhD from a Swiss university. Schirnhofer followed suit. Both gained their doctorates in philosophy.

In The Gay Science, he notes how monstrous it is that young women are brought up told that sex is shameful and sinful

In 1882, Nietzsche fell completely and drastically in love with Lou Salomé, who would later enchant both Rilke and Freud. During this period, he wrote about the psychological dilemma of women. In The Gay Science, he notes how monstrous it is that young women are told that sex is shameful and sinful, only to be hurled into marriage and propelled by the man they are taught to worship as a god into the terror and duty of sex. How are they expected to cope? “There,” he observes, “one has tied a psychic knot that has no equal.”

I had no idea Nietzsche could be funny until I read his letters. “The gentlest, most reasonable man may, if he wears a large moustache, sit as it were in its shade and feel safe,” he wrote, self-mockingly. “As the accessory of a large moustache he will give the impression of being military, irascible and sometimes violent – and will be treated accordingly.”

Condemned by ill health and abysmal eyesight to convey his philosophy in short, aphoristic bursts, Nietzsche knew the power of raising a bubble of laughter, only to puncture it as you ponder the further meaning: “Is man God’s mistake, or is God man’s mistake?” “Man does not strive for happiness; only the Englishman does that” – a dig at Jeremy Bentham and John Stuart Mill. “Possession usually diminishes the possession.” “Never trust a thought that occurs to you indoors.” He even makes fun of his readers: “The worst readers are those who behave like plundering troops: they take away a few things they can use, dirty and confound the remainder, and revile the whole.”

Nietzsche is an unusual philosopher because he doesn’t tell us what to think. There’s no such thing as Nietzsche-ism. He sums it up in one of his aphorisms: “You repay a teacher badly by becoming merely a pupil.” In other words, read me but think further.

As for the myths that have grown up around him, the last word surely should belong to the man himself. “I am frightened,” he wrote, “by the thought of what unqualified and unsuitable people may invoke my authority one day. Yet that is the torment of every teacher … he knows that, given the circumstances and accidents, he can become a disaster as well as a blessing to mankind.”

• I Am Dynamite!: A Life of Friedrich Nietzsche is published by Faber. To order a copy for £21.50 (RRP £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.