Versatility in an author, normally viewed as an admirable quality, somehow came to be regarded with suspicion in Primo Levi. Those who were happy to accord him the highest respect as exponent of ‘witness literature’ for his harrowing account of Auschwitz in If This Is A Man, or his more relaxed account in The Truce of the endless train journey back to Italy after liberation, were dismayed when collections of playful sci-fi or fantasy tales, like Lilith And Other Stories, were made available in English. Some baffled reviewers resorted to expressions like "scraping the barrel".

The whole barrel is now on display in these three handsome volumes, and they will allow readers, at least those with deep enough pockets, to judge Levi’s output in all its varied entirety. They come complete with a useful chronology of his life, discussions by some of the translators and highly informative essays on the inspiration and gestation of the individual works as well as of their gradual success in the world. Each book has been freshly translated, except for If This Is A Man, which has been revised by the original translator, Stuart Woolf, who had the insight to detect the value of the work when it was still unsung, and who was able to work with the author on the translation.

The effect of reading Levi’s work one after the other is akin to walking around the Uffizi galleries in Florence, readjusting expectations and experiences from room to room. The need to make people understand the savagery of Nazism was life-long. The Drowned And The Saved, his last work, returned to the theme but widened out to become a philosophical enquiry into human evil. At the same time he was a professional writer who wrote reviews, essays, poems, introductions, one novel, an unclassifiable monologue work (The Wrench) and critical essays on authors from Rabelais to Aldous Huxley, as well as fantastic tales on the origin of centaurs or the attendance of a kangaroo at a stylish reception, not to mention articles on chemistry, the subject he studied at university and the field in which he worked.

Sometimes he felt the need for disguise, so Natural Histories, his first collection of imagined tales, was published under a pseudonym, Damiano Malabaila, while at other times he identified himself with the centaur, for his double nature as scientist and writer, or with Coleridge’s Ancient Mariner for his urge to stop indifferent passers by and compel them to listen to his ‘ghastly tale'. His one anthology of poetry is given the Coleridgean title At An Uncertain Hour.

Not even his most fervent admirers will regard him as a great poet, but he always wrote verse. He was a surprisingly private man who revealed little of himself even when recounting his own experiences, but poetry demands and facilitates access to hidden regions of the psyche. His poems have been sensitively translated by Jonathan Galassi. February 11, 1946 is, in spite of the bleak opening stanza, both a love poem and a fundamental statement of belief. Levi proposes, but then jettisons, the idea that the cosmos is an amoral, accidental chaos:

"I contemplated the mad blasphemy

That the world was one of God’s mistakes

And I was one of the world’s…"

The tone turns more defiant in the second part of the poem when he addresses Lucia Morpurgo, the woman he would marry:

"I shouted no with every fibre

That I wasn’t through

That I still had too much to do

It was because you were there in front of me…

I came back because you were there."

"Came back", not from the concentration camp, but back to the sun, back to life, back to execute the duty of expressing the unspeakable, back to the world of men and women, even if he was never quite at home there. It is right to accord him prime place in the 20th-century genre of testimonial literature for his accounts of the enormity, not banality, of evil which was the Nazi concentration camp. The requirements of this type of writing were inflexible, he believed, and precluded any attempt at inventiveness. He wrote that without the experience of Auschwitz, he would not have become a writer, which is doubtful, but also that “in Auschwitz I became a Jew”, by which he meant that the systematic degradation he endured compelled him to accept an identity to which he had not been given much thought. It also invited him to accept the rich Jewish cultural, but not religious, heritage. He was never able to reconcile the existence of God and Auschwitz.

For all the blackness that is present in his work, Levi was a frustrated optimist and certainly no pessimist. He rejected the idea that Auschwitz showed that humans were intrinsically prone to evil. Equally, he always defined himself as a humanist, not in the restricted sense that word has acquired in English but in the bolder Renaissance sense of one who believes in the dignity of humanity. At times he said that he had written If This Is A Man impulsively, with no thought of structure, but it is not true. At the core are two significant chapters, the first one an examination of his competence in chemistry by the German Dr Pannwitz. His success and the consequent employment indoors saved his life, but as he exited from the laboratory, a guard casually wiped his hands on Levi’s shirt, a gesture Levi judged as defining the contempt in which he was held.

The following chapter, deliberately placed to counterbalance the previous episode, is among the most life-affirming statements in modern literature. As he walks with a companion to collect the soup that was the prisoners’ food, he attempts to recall the canto in Dante which describes the plight of Ulysses, the heroic figure placed in hell for treachery but the very incarnation of the indomitable human spirit. In ringing rhetoric, Ulysses challenges his men to sail beyond the Pillars of Hercules, to venture beyond the boundaries set for humankind and to prove that they were "born not to live as brutes but to follow virtue and knowledge". Even at the darkest moments, Levi affirmed these values.

In this he differed from Kafka, on whom he wrote several essays and whose novel The Trial he translated at the request of his publisher who thought that the encounter between the writer who is held to have foreseen the horror ahead of European humanity and the man who endured it would be rewarding. In fact, however successful the translation, the experience was disastrous for Levi, and such was the distaste he felt for Kafka’s vision that working on his novel brought on one of his intermittent spells of depression. In an essay reflecting on translating Kafka, he commented that the difference in the underlying beliefs of the two was that while he himself "always tended towards a transition from obscurity to clarity", Kafka takes "the opposite approach".

Levi regarded obscurity of style as bad manners and for that reason stated bluntly that he "could not stand Samuel Beckett". His ideal was the scientific report, where matters were stated coherently and clearly. His own style was more complex than that statement allows, but his fearless clarity guarantees him a pre-eminent place among the great ‘wisdom writers’ of our time, the man who had looked into the mouth of the beast but held to a belief in human potential for goodness and who even proposed a moral vision for today. "I believe in reason and discussion as supreme tools for progress, and so I place justice before hatred." This was a man.

The Complete Works Of Primo Levi (three volumes), edited by Ann Goldstein, is published by Penguin Classics, priced £120