In Kurt Vonnegut's 1961 novel Mother Night, an affectless German-American named Howard W Campbell Jr is ensnared in the great ideological conflicts of the 20th century.

The plot need not concern us. It is enough to say the apparent Nazi surrenders to Israeli justice, that while in prison he encounters Adolf Eichmann, and that his tale has a moral.

Vonnegut was very clear about the last detail. In fact, lest he be misunderstood, he stated his moral on the first page of his novel's introduction and repeated it periodically: "We are what we pretend to be, so we must be careful about what we pretend to be."

Eichmann makes only a brief appearance in the fiction. Campbell, a playwright, gives the mass killer advice on the writing of an autobiography. The joke is typical Vonnegut. The real SS-Obersturmbannfuhrer Otto Adolf Eichmann really did compose memoirs after being snatched from Argentina in May 1960 by agents of Israel's Mossad. More than that, he was truly careful about what he pretended - or perhaps believed - himself to be.

In the novel, Eichmann tells Campbell that life has phases. "Each one is very different from the others, and you have to be able to recognise what is expected of you in each phase." In return the playwright, a deniable spy for America, says the architect of the Final Solution "cannot distinguish between right and wrong - that not only right and wrong, but truth and falsehood, hope and despair, beauty and ugliness, kindness and cruelty, comedy and tragedy, are all processed by Eichmann's mind indiscriminately..."

The political theorist Hannah Arendt, who reported on the Nazi's trial for the New Yorker, had made a famous phrase of the conundrum: "the banality of evil". It became, as it remains, one of the central mysteries of the Holocaust: how did so many dull, ordinary, undistinguished individuals discover the capacity for murderous depravity on a vast scale and seem not to realise what they had become?

Bettina Stangneth's brilliant portrait of Eichmann, once the Nazi given charge of "Jewish Affairs", has the puzzle at its core. Its subject manipulated reality like a series of fictions. He lied, of course, and did so relentlessly while in hiding in South America. But he also celebrated his capacity for "re-invention", did not once repent, and "processed" his hideous truths, as Vonnegut had it, with ease. Eichmann, who fancied himself an author, rewrote the story of existence relentlessly. Yet real people suffered real deaths in their millions at his hands.

After his capture, Eichmann followed a script that was already familiar: he had not been an important Nazi, he had played no part in the decision to exterminate Jews, he had - in the infamous phrase - only followed orders. Vonnegut's novel, a meditation on what such excuses can ever mean, found its moral in that.

Stangneth, with a hoard of newly released archives at her disposal, documents another fiction. Eichmann was insane: an inescapable assumption. But he moulded the world to his own endlessly creative madness. Why not? Hitler's Reich had shown how completely, how easily, that could be done. So is that the authentic nature of genocide?

An irony attends Stangneth's pursuit: you will find no mention of Vonnegut or of Mother Night in the index to Eichmann Before Jerusalem. This piece of non-fiction does not acknowledge, far less imitate, art. Instead, the author engages, more or less explicitly, with Arendt's 1961 portrait of a mass murderer during his rendezvous with justice, one that influenced Vonnegut and many others besides.

Here was Eichmann, ironically enough, in the mirror of his own choosing: the bureaucrat as nonentity, the apolitical, anonymous - truly banal - character who had been given a job and simply done it to the best of his abilities. Arendt's suggestion, implicit and explicit, was that the impulse to genocide comes from common clay, not from some supernatural eruption beyond the limits of humanity. It remains a profoundly troubling idea.

Yet Stangneth demonstrates, with great forensic skill, that the metaphysical construct, the bedrock of Eichmann's defence before an Israeli court, was and is rubbish. Here was a conviction Nazi, not some witlessly obedient "apolitical" pen-pusher. This one was a proud National Socialist from the beginning and he stayed that way long after 1945. The man who could boast, in his exile, of the slaughter of 400,000 Hungarian Jews as an "achievement" was in no sense a victim. He was cunning enough, however, to shape and reshape the narrative of poor, luckless Otto Adolf.

As Stangneth recognises, obsessive duplicity is one clue to guilt. Who lies for decades, lies until the moment of execution, if they regard themselves sincerely as nothing more than fate's plaything? You need read only The Nuremberg Interviews (2004), conducted in the war's aftermath by the US Army psychiatrist Leon Goldensohn, to enter a bizarre universe. In their accounting, none of these senior Nazis were to blame for six million deaths. No one was culpable. "Morally", then, the Holocaust might as well never have happened.

Eichmann was a master in this black art, manipulating audiences and anecdotes alike. But when his listeners happened to be a bunch of old Nazis in Buenos Aires, and his interviewer a Dutch fascist journalist named Wilhelm Sassen, hubris got the better of the killer, as it does in all the best novels. His admirers hoped that Eichmann would feed their fantasies and their need for excuses. Instead, though he denied it later, he confirmed all, every appalling detail, and boasted of his role.

The Sassen interviews have had a contested history for many years. Some, like Eichmann himself, have tried to maintain that the transcripts and tapes were still another form of fiction. Stangneth wades through the murk: these were indeed the words of a "fanatical warrior" (as he claimed) for the ideology of racial extermination. He meant every one of those words. He had known exactly what he was doing at every step along the way.

Two fictions are thereby destroyed. One is Eichmann's, the other Arendt's bleak belief that any human can become a functionary in a murderous bureaucracy. There is not much comfort, for all that, in the truth that remains, or in a secondary theme pursued by Stangneth. Even once the facts of the Holocaust were known, blind eyes were turned, time and again, to the surviving old Nazis around the world and their machinations. The victors chose to overlook a malignancy they had never understood.

Stangneth's Eichmann is a man "desperate to write and explain himself", to wash away reality beneath torrents of words. For the Nazi, truth and lies became mere categories of art. What was said mattered less than how it was said, and to whom. The facts, vast and grim, counted for nothing beside what was believed. That could only be achieved, in the ultimate exercise of power, by a fascist's bottomless conviction.

At the end of Vonnegut's Mother Night, Campbell is vindicated and offered freedom. He finds the prospect "nauseating". Instead, he demands suicide: "I think that tonight is the night I will hang Howard W Campbell Jr, for crimes against himself." Otto Adolf Eichmann would have found the idea baffling.