Hanns and Rudolf: The True Story of the German Jew Who Tracked Down and Caught the Kommandant of Auschwitz. By Thomas Harding. Simon & Schuster; 348 pages; $26. William Heinemann; £20. Buy from Amazon.com, Amazon.co.uk

HANNS ALEXANDER was a Jewish refugee from Germany, a soldier, a banker and a bit of a prankster. But until he died in London in 2006, few beyond his close family knew of his years as a Nazi hunter. His biggest prize was tracking down and arresting Rudolf Höss, the man who ran the Auschwitz death camp. This late revelation inspired Thomas Harding, Alexander’s grandnephew, to explore the lives of these two men, which he chronicles in a gripping new book, “Hanns and Rudolf”.

Rudolf (the book uses the men’s first names) is the more familiar figure. As a young man he thought he would become a priest, but he came of age in uniform instead, fighting in the Middle East in the first world war. The young veteran signed up early to the Nazi party after hearing Hitler speak, but dreamed more of soil than of blood: he wanted to farm, and the SS gave him the chance to manage a stable.

But his responsibilities evolved, steadily, darkly. Heinrich Himmler summoned him to help administer Dachau, the first concentration camp. Auschwitz came later and Rudolf oversaw the killing of many people, more out of duty than inclination, or so he told himself. Between 1m and 1.5m are believed to have died at Auschwitz. In a final letter to his wife, he called himself “the greatest of all destroyers of human beings”. Yet his memoirs, written while he awaited trial in Warsaw, lament that readers “would never understand that he, too, had a heart, and was not a wicked man.”

Mr Harding does not change existing views of Rudolf, a man Primo Levi described as more stupid than Adolf Eichmann, a fellow Nazi architect of the Holocaust, but not a sadist. Yet he has unearthed chilling details of Rudolf’s family life at his Auschwitz villa, largely from interviews with his daughter, Brigitte. Mr Harding relates that the Höss children played at being Kapos and inmates, wearing replicas of prisoners’ armbands created by the family seamstress. The master bedroom afforded views of the camp.

Mr Harding also impressively recovers Hanns’s story. The son of a prominent Berlin doctor, he followed his father to England in 1936, joined the army and landed in Normandy six weeks after D-Day. Hanns’s fluent German won him assignment to the first War Crimes Investigation Team. His encounter with the newly liberated concentration camp of Bergen-Belsen, where he helped bury the corpses, made him zealous. Hanns first hunted down the vicious administrator of Luxembourg, Gustav Simon, in a pursuit that makes for dramatic reading. He finally cornered Rudolf after threatening his wife to send their 16-year-old son off to Siberia.

The stories of these two men finally intersect in 1946 at a stone barn in Gottrupel, Germany, near Denmark. After the arrest, Hanns left Rudolf alone for ten minutes with the vengeful search party. The horrors Hanns witnessed at Bergen-Belsen had turned him “fierce to the point of brutality with those he interrogated, and full of hate,” writes Mr Harding. Rudolf was ultimately hanged at Auschwitz.

Mr Harding begins his book with a promise to challenge “the traditional portrayal of the hero and the villain”. Fortunately his narrative is not so morally muddy. Rudolf is shown as a man who, owing to circumstance and character, embraced evil. Hanns did the opposite.