The SS-Einsatzgruppen

and the Invention of the Holocaust.

By Richard Rhodes.

Illustrated. 335 pp. New York:

Alfred A. Knopf. $27.50.

THE main goal of the German Einsatzgruppen during World War II was to turn the Jews in the Soviet Union into landfill.

In large measure, they did. Having raced in behind the invading German Army in June 1941, these mobile killing squads proceeded to fill ravines, quarries, trenches, ditches and pits in Russia, Belarus, Ukraine, Lithuania, Latvia and Estonia with the bodies of more than 1.3 million Jewish men, women and children.

When most of us think of the Holocaust we think of Auschwitz. But the industrialized, largely hands-off method of killing Jews at Auschwitz and the five other gassing centers in Poland was developed to a great extent because of what the German leadership saw as the too hands-on experience of the Einsatzgruppen in the Soviet Union -- individual bullets shot into individual Jews by individual Germans, or by the local police they oversaw. In Babi Yar, a ravine in Kiev, the Einsatzgruppen shot 33,771 Jews in just two days. The work was bloody and sometimes, even for these hardened killers, demoralizing. Auschwitz was the final solution to the Final Solution.

''Masters of Death'' illuminates this early and pivotal chapter of the Holocaust. In it, Richard Rhodes -- the Pulitzer Prize-winning author of, among many books, ''The Making of the Atomic Bomb'' -- focuses on the experience of the victims and on the methods and personalities of the killers. And he shows how the enterprise of individualized murder led to the enterprise of industrialized murder. Through his fine and accessible account, Rhodes deepens our sense of the Holocaust's utter evil. But, in one way, he also confounds it. Using a theory of violence to which he has become attached in recent years, he tries to explain how that evil came about. And in that attempt he falls short.

That Rhodes was drawn to examine the Einsatzgruppen is hardly surprising. He has long been interested in the problem of violence, and theirs was perhaps the ultimate example -- vast, repetitive and daily, and characterized by a close proximity to the victims. For the Einsatzgruppen, murdering human beings was primarily a problem of logistics, engineering, efficiency.

In fact, how they approached some of their technical challenges illustrates what they did and who they were. For instance, when people who were shot at the edge of a pit would fall in, on top of those who had been shot a few moments earlier, their bodies would crumple every which way. This resulted in unused -- and therefore, from the point of view of efficiency, wasted -- space between the bodies. It meant digging more pits than if the bodies had fallen into neat rows.

Rhodes describes how Friedrich Jeckeln, an SS and police general, solved this problem. Jeckeln called his solution Sardinenpackung -- sardine-packing. ''Today we'll stack them like sardines,'' he informed a colleague at a killing site in western Ukraine. As that colleague later described it, ''The Jews had to lie layer upon layer in an open grave and were then killed with neck shots from machine pistols, pistols and rifles. That meant they had to lie face down on those previously shot.''

And here was another logistical challenge the Einsatzgruppen overcame: shooting women holding infants. How do you kill both at the same time? One solution to this problem, Rhodes explains, was devised at a killing site in Latvia: mothers with infants had to hold their babies over their heads; one man shot the mother, one the child.

Rhodes notes that more than a few of the killers enjoyed their duties. A woman from a town near Minsk saw a young German soldier walking with a year-old baby impaled on his bayonet. ''The baby was still crying weakly,'' she later recalled. ''And the German was singing.'' In some sites in Lithuania, after ''Jewish actions,'' schnapps was distributed and group photos were taken. Often, the killers celebrated with dinner parties at local inns.

And, after the war, a Krakow police official testified that members of the border police were, with some exceptions, ''quite happy to take part in shootings of Jews.'' The official went on: ''They had a ball! . . . Nobody failed to turn up.''

But for many of the killers it was, in fact, a difficult task. Heinrich Himmler, the head of the SS, who was in charge of the project of murdering all Jews and who, as Rhodes notes, witnessed some of the killings himself, was troubled by what such individualized killing might do to his men. True, he frequently exhorted them to be ''hard'' -- though the work was unpleasant, he said, it was necessary for the future of Germany. But he wanted to find a way to ease the psychological burden on his men. This was accomplished first by gas vans, which were more impersonal, and then by the still more efficient gas chamber system, in which Germans could release gas into vast spaces filled with Jews and force other Jews to pull out the corpses before gassing them in turn.

How could the ''ordinary men'' of the Einsatzgruppen have done all this? What explanatory theory can possibly account for it?