In the summer of 1942, Albert Speer visited Adolf Hitler at the Führer’s field headquarters in the Ukraine. “One quiet evening,” Mark Mazower writes in “Hitler’s Empire” (Penguin Press, 726 pages, $39.95), Hitler dilated to Speer on his favorite subject: what the world would look like after the German victory, which he still believed was inevitable. By the end of the year, he predicted, the Wehrmacht would have taken the Soviet Caucasus. “If in the course of the next year we manage to cover only the same distance … by the end of 1943 we will pitch our tents in Teheran, in Baghdad and on the Persian Gulf,” Hitler gloated. He went on to do a back-of-the-envelope calculation of how many Germans would be available to colonize this vast new territory. Combining true Germans with their racial “cousins,” such as the Dutch, Hitler, Mr. Mazower writes, came up “with a grand total of 127 million real or potential Germans … [and] then started projecting birth rates far into the future.”

In this mad monologue, Mr. Mazower finds a perfect snapshot of the irrational forces that both created Hitler’s brief empire and led to its destruction. What Hitler craved, Mr. Mazower makes clear, was a territorial tabula rasa on which he could write his racial and imperial fantasies. Just as Europeans had once supplanted the Indians in the Western Hemisphere, so Aryans would drive out the subhumans who populated Eastern Europe: Poles, Ukrainians, Byelorussians, and especially Jews. Once these peoples were exterminated or reduced to slavery, their lands would be colonized by German pioneers — 20th-century versions of the medieval Teutonic Knights, living as warrior-farmers on feudal estates.

The Nazis never did get as far as Baghdad, of course, nor did Hitler have the chance to build the titanic monuments to himself that he dreamed about — for instance, the supersized Golden Gate Bridge that was to stretch across the Elbe, “so that Germans entering Hamburg by sea would say: ‘What is so extraordinary about America and its bridges? We can do just the same.'” But between 1938, when Germany swallowed up Austria and part of Czechoslovakia without firing a shot, and 1942, when the tide of war began to turn against the Wehrmacht in Russia, Hitler did manage to bring more of Europe under his control than any conqueror since Napoleon.

Mr. Mazower tallies his conquests: “Germany occupied approximately one-third of the European land-mass and ruled nearly half its inhabitants. The swastika flew over the Channel Islands in the west and over Mount Elbrus in the Caucasus, from northern Norway to the Sahara.” Yet just three years later, not only had Germany lost all its conquests, but it was itself conquered, and its eastern half would remain under Soviet occupation for the next half-century.

How did the Nazis rule in the empire they so quickly and unexpectedly won, and what did they hope to do with it in the thousand-year Reich that never was? Why did nemeses follow so quickly on their hubris? In “Hitler’s Empire,” Mr. Mazower, a professor of history at Columbia University, gives thoughtful answers to these questions. Drawing on an enormous amount of research, yet always writing clearly and well, Mr. Mazower takes the reader on a guided tour through every corner of the Nazis’ domains. He examines their economic policies, their diplomatic strategies, and their internal debates over the future of Europe. At the same time, he reports the gassings, shootings, starvation, deportation, torture, and rape that the Nazis inflicted, in various degrees, on almost every people they ruled.

But while the Nazis destroyed whole towns in occupied France, Bohemia, Greece, and even Italy (after the collapse of Mussolini’s government), it was in the East that their imperial fantasies truly ran wild. The difference can be explained by the racist ideology which drove Nazism from the beginning. While Hitler treated the French as enemies to be defeated, he saw the Slavs as a demographic threat to be eradicated. In this, Mr. Mazower shows, the Nazis were following a tradition of German thought that stretched back to before World War I. As early as Bismarck’s time, there had been a Royal Prussian Colonization Commission to settle German farmers in the country’s majority-Polish eastern provinces. When Himmler declared that he wanted to “build a blond province” in what used to be Poland, he was restating an old German ambition in biological terms.

Yet it was precisely this element of biological racism in the Nazis’ worldview that made them a different kind of imperialist. No Prussian bureaucrat could have invented a scheme as diabolical as Himmler’s Lebensborn program, in which the SS kidnapped Polish children who appeared Aryan and gave them to German mothers to raise. This was what Himmler called “see[ing] to it that none of our blood is ever lost to the outside world.” Mr. Mazower chronicles the embarrassments that the Nazis’ crackpot racism brought on them, when they realized that there simply were not enough Germans to settle the territories they had conquered. Albert Forster, the Gauleiter of Danzig, solved the problem by simply declaring that most of the Poles under his control were actually “Kashubians,” a different racial type that was not Slavic but “ripe for Germanization.”

More important to the Nazis than creating new Germans, however, was getting rid of non-Germans. General Plan East, the Nazis’ blueprint for Eastern Europe, called for murder on a scale undreamed of in human history. Mr. Mazower quotes Erhard Wetzel, a Nazi “race expert,” who estimated that Germanizing the East would require getting rid of “some 60-65 million people,” starting with 20 million Poles, who were “the most dangerous of all the alien ethnic groups which the Plan envisages for resettlement.” When the Germans launched Operation Barbarossa, the invasion of the Soviet Union, in 1941, Goering looked forward to “the biggest mass death in Europe since the Thirty Years War.” Some planners in the SS, where the younger, more ideological, and visionary Nazis tended to congregate, did not want to stop even at the Urals, the traditional border between Europe and Asia. Wetzel was already worried about the race war that would ensue when German colonists brushed up against “a Great Asia and an independent India,” which “posed a greater long-term threat to Europe’s racial purity than even the Slavs.”

Moments like these underscore one of the major themes of “Hitler’s Empire,” which is that the Holocaust, now remembered as the greatest of the Nazis’ crimes, was actually just a prelude to what they had in mind. Because of the central role of anti-Semitism in Nazi ideology, the Nazis made the extermination of the Jews their first priority. But there is every reason to believe that the techniques the Nazis perfected in the Holocaust would have been used, in the event of a German victory, to clear all of Eastern Europe for German settlement. Poles and Ukrainians who eagerly assisted in killing Jews in 1941-2 began to realize, as the war stretched on, that their turn might be next. Mr. Mazower quotes one German officer in Poland who explained that the Polish resistance was fueled by the Poles’ belief that the Holocaust offered “an atrocious picture of their own destiny.” Reinhard Heydrich, the SS ruler of what had been Czechoslovakia, spoke of sending millions of Czechs to Siberia — a clear echo of the euphemism used for the Jewish genocide, “resettlement in the East.”

What strikes the reader most forcibly in “Hitler’s Empire” is the bizarrely casual way in which the Nazis disposed of lives and nations. They lacked respect, not just for human life, but for reality itself; as Hannah Arendt put it, their totalitarianism was an “experiment against reality.” Especially after the amazing victories of 1940, Hitler believed that anything he desired could be made to happen. This nearly psychotic grandiosity helps to explain the consistently self-defeating quality of Nazi policy in so many areas explored by Mr. Mazower. Hitler killed millions upon millions of Jews and Soviet POWs, even as the Reich faced severe labor shortages; he treated the Poles and Ukrainians as slave races, instead of enlisting them as allies against the hated Soviets; he refused to allow the Wehrmacht to fall back to defensible positions, insisting that tactical retreat was equivalent to treason. In all these ways and more, Mr. Mazower shows, the ideology that fueled Hitler’s empire also ensured its swift destruction.

akirsch@nysun.com