Once, the Holocaust had an almost sacral quality: It was approached with fear and trembling as a cataclysm beyond comparison. Now the tendency is to think of it not as something distinctive but as something representative. What, after all, made these killings any more horrific than the tens of millions of others during World War II—on battlefields and in prison camps, in forests and over ditches, in bombed cities and wasted fields? How is the Holocaust different from other genocides? Was Hitler’s murder of six million Jews so different in kind from Stalin’s deliberate terror-famine in the Ukraine in 1932-33 that left three million dead?

Such questions lie in the background of the Yale historian Timothy Snyder’s remarkable “Black Earth: The Holocaust as History and Warning,” a book that extends his gripping, somber “Bloodlands: Europe Between Hitler and Stalin” (2010). In that volume’s account of purges, massacres, shootings, starvations, executions and incinerations in Germany, the Soviet Union and the contested lands in between, the Holocaust is but a subset of 14 million gratuitous yet calculated murders. In “Black Earth,” the Holocaust is the focus of attention, but we are never allowed to forget the surrounding charnel house. Mr. Snyder said that in “Bloodlands” he wanted to write a “transnational” history, taking a broad look at events from without rather than from within the world of a particular nation. “Black Earth” takes a similarly broad approach: He does not see the Holocaust as a “war against the Jews”—as the historian Lucy Dawidowicz called it—for which Hitler was prepared to sacrifice ordinary military strategy, but as an extreme example of Hitler’s wide-ranging racial obsessions.

One consequence of this approach is that the evil of the Holocaust comes to seem more organically connected to the excruciating barbarity of the bloodlands. It also alters—without eliminating—the nature of its singularity. These issues made some readers of “Bloodlands” uneasy because of a long tradition of Holocaust interpretation that, in its most vulgar form, denies either its extremity or its Jewish particularity. In the postwar Soviet Union, for example, no group, particularly not the Jews, merited special Soviet commemoration—not even at Babi Yar, the ravine outside Kiev where some 34,000 Jews had been lined up and shot by SS troops in 1941. The Soviets treated the Warsaw Ghetto uprising of 1943 as a rebellion by Communists rather than by imprisoned Jews, and they associated the Nazi death camps with the epic martyrdom of Soviets and Poles. And there were plenty of examples: a million residents of Leningrad starved to death during the Nazi siege, 3.1 million Soviet prisoners of war were shot or deliberately starved to death by the invading Germans.

A similar resistance to particularity took root in the West as the Holocaust made its way into school curricula, museum exhibitions and popular consciousness. The subject is now usually treated as a prelude to a general discussion of genocide. Broadly prescriptive lessons and homilies are proposed that will, supposedly, make another Holocaust unlikely, urging tolerance or more empathetic attitudes toward minorities. The more Holocaust education there has been, it seems, the more often the Holocaust is casually invoked in trite or meretricious comparisons.

Mr. Snyder avoids such pitfalls, and “Black Earth” is mesmerizing. It is not a conventional history. As he surveys what took place, Mr. Snyder highlights lesser known events in order to discover anomalies, phenomena that need exploration or explanation. He begins with a disturbingly vivid foray into Hitler’s mental world. He looks at the prewar attitudes toward Jews, including the eccentric approach of Poland, which was thinking, in the 1920s, of sending Jews to Madagascar and, in the 1930s, actively trained and supported Revisionist Zionist groups in the hope that they would lure Jews to a national home in Palestine. Then the Nazis took over, murdering some three million Polish Jews. In describing the era of these killings, Mr. Snyder is sometimes mordant, often shocked, always probing.

Why has Auschwitz become the archetypal symbol for the Holocaust when it was not even, like Treblinka, a dedicated death camp and when its technique of mass killing was the third one developed by the Nazis and the third in significance? (The most important, which killed the most Jews and showed the feasibility of the Final Solution, was shootings over pits.) Why did 99% of the Jews in Nazi-occupied Denmark survive while 99% of the Jews in Nazi-occupied Estonia were murdered? And why were the death camps, shootings and gassings located in Eastern Europe?

Mr. Snyder’s account ends up shifting the Holocaust’s center of gravity to Eastern Europe and the countries that then lay between Germany and the Soviet Union: Poland, the Baltic republics, Belarus and the Ukraine. This region is his specialty; he has a knowledge of at least 10 languages and consulted sources in German, Polish, Russian, Ukrainian, Belarusian, Yiddish, Czech, Slovak, French and English. This is something no other chronicler of the Holocaust has done. In fact, Mr. Snyder writes, the founding scholars of Holocaust studies did not even use Eastern European languages in their work: Raul Hilberg’s parents spoke Polish; he didn’t. Saul Friedländer comes from Prague, yet doesn’t employ Czech sources. “No major historian of the Holocaust,” Mr. Snyder notes, “learned an east European language after 1989.” Yet this is where the Holocaust began, with the systematic killing of Jewish men, women and children in Ponary Forest, avidly assisted by local Lithuanians. This is where, in Mr. Snyder’s telling, the Holocaust itself took place.

What was it about Poland or Belarus that made them so hospitable to participatory mass murder? The usual explanation is anti-Semitism—“a historically predictable outburst of the barbarity of east Europeans,” Mr. Snyder writes. But “the level of antisemitism, insofar as this can be ascertained, does not seem to correlate with Jewish death rates.” Lithuania, where the Final Solution was eagerly pursued by locals, had a right-wing dictatorship before the war, but it was not an anti-Semitic one; in fact, its leader declared his opposition to Hitler’s “zoological nationalism and racism.” Lithuania even had a reputation as a refuge; in 1938-39, some 23,000 Jews fled from the Soviet Union and Germany into Lithuania, which welcomed them as no Western nation would. None of this mitigated the virulence of what followed.

Hitler had, from the very start, imagined the German empire expanding across Eastern Europe into the Soviet Union. But in 1939, buying time and territory, he made a pact with Stalin, the two dividing the intervening lands between them. Germany took chunks of Poland; the Soviets swept through the rest, along with Lithuania, Latvia, Belarus and other territories.

Just before the war, during Stalin’s Great Terror, supposedly nefarious Polish agents were hunted throughout the Soviet Union, leading to the shooting of more than 100,000 Soviet citizens with a Polish background—the largest “peacetime ethnic shooting campaign in history,” Mr. Snyder notes. So the Soviet Union was hardly going to be hesitant when it took over Polish territory. Within months of the invasion, almost half a million Polish citizens were deported to the Gulag and 21,892 were summarily shot in the Katyn Forest and at other sites. Lithuania and Latvia were demolished as nations, dissolved into the Soviet Union.

The Germans were even more ruthless when they set up shop. Hitler called for a “massive extermination of the Polish intelligentsia,” suggesting that a “resolution of the Polish problem” would be reached with murder. Polish children were deliberately taught a pidgin German so they “would be distinguishable as racial inferiors but capable of taking orders.” By 1941, most Polish Jews in Western Poland were behind ghetto walls. Within another year, most were dead.

In June 1941 came Hitler’s surprise attack on the Soviet Union. No sooner had the Communist purges taken place throughout Soviet-run Eastern Europe than the Nazi ones began. The Soviets had destroyed the state apparatus in each territory. Now it was upended again. But often the same local leaders were involved in managing both upheavals. Anybody with authority in the Soviet regime had to quickly dissociate himself from the past and demonstrate a new allegiance. The killing of Jews was a solution. The massacres were, Mr. Snyder suggests, a kind of “political scenography” in which the local population proved itself to its new masters, shedding its Soviet past. This expiation was often made explicit: Nazi ideology identified Judaism with Bolshevism, so the murder of Jews was a form of revenge against the onetime occupiers.

That these were “consecutively occupied lands,” Mr. Snyder argues, is the crucial fact. Whether locals would eagerly participate in the murders and how thoroughly the Final Solution would be pursued were matters determined not by the extent of local anti-Semitism but by the condition of each nation-state. The entire Holocaust took place on lands touched by Soviet power and then again by German power. It was the strategy of the Nazis to begin with “state destruction” wherever they conquered. But Germans only killed Jews, in Mr. Snyder’s interpretation, if the local state had been destroyed even before they arrived. Even Jews in relatively tolerant urban settings like Minsk, Lodz or Riga would then be readily massacred, in expiation and demonstration. Bureaucracy, Mr. Snyder argues, didn’t allow the Holocaust; the lack of bureaucracy did.

This is a startling interpretation, and it will take some time for Mr. Snyder’s account to be scrutinized by scholars. But I am not entirely convinced by his conclusion that state power is the crux. It clearly matters what kind of state is coming into power and what kind of state is losing it. Germany, after all, demonstrated that state power can be harnessed for organizing mass murder. Today, ISIS has proved that a well-run organization with a system of law can institutionalize atrocity. There is also a hint of circularity in Mr. Snyder’s formula: If state power is the creator of social order, then of course the lack of state power would mean the end of social order. The destruction of authority results in a lack of authority.

But the wartime massacres didn’t take place solely because there was no state structure; they happened because the lack of authority accompanied fervent anti-Semitic convictions. Anti-Semitism should not just be thought of as a form of racism or prejudice. It is a deeply held belief, religious in its power, through which the world’s events are interpreted. Expressions of furious hatred are not merely choreographed passions staged for new masters.

Mr. Snyder makes the character of Hitler’s anti-Semitism clear in his opening chapter. For Hitler, all of history was an amoral battle of disparate races struggling for space, land and power. But, in Hitler’s cosmology, the Jews were not another competing race. They were “a spiritual pestilence” that corrupted the entire species, disrupting the forces of nature. The Jew was the embodiment of original sin, the “destroyer of Eden.” Hitler believed that the Jew might convince all the races that they were equal and, more dangerously, that they should value “universalism” over the particular. How could anyone have believed this vulgar Nietzscheanism—as Hitler surely did—and not have pursued a Final Solution? Similar ideas provided the fertile ground in Eastern Europe when the Nazis arrived. In leaving this issue relatively unexplored, Mr. Snyder takes transnationalism too far.

This is important. The Holocaust, like no other act or example of human evil, has inspired legions of lessons and “warnings,” as if they were required to justify the attention. The enshrinement of “tolerance” is only the most egregious example, but the Holocaust didn’t take place because of intolerance, and it would not have been prevented by tolerance. Why the compulsion to make comparisons with other atrocities? It would be like concluding a history of World War II by emphasizing that there were other deadly wars too, and we should all learn to be peaceful creatures. Somehow, in the case of the Holocaust, this approach has become conventional. Why the persistent straining at homily? Is there an element of shame involved? And why is the Holocaust so relentlessly invoked in irrelevant situations? Is that, too, some form of self-exoneration or alibi?

I wondered about some of this when encountering Mr. Snyder’s last chapter, “Our World.” He writes: “The planet is changing in ways that might make Hitlerian descriptions of life, space and time more plausible.” He suggests that now, as then, there is a sense of imminent apocalypse. Just as the Jew disrupted the global ecology for Hitler, something has now “diverted nature from its proper course.” And it may well cause a similar series of events. What is the contemporary threat? Climate change. And the irony, Mr. Snyder suggests, is that it could again place Jews in a precarious position. Mr. Snyder points out that the Holocaust proved the need for a strong nation-states, and Israel’s existence is essential for Jewish survival. But, he argues, “the continuing desertification of the Middle East might generate both regional conflict and the demand for scapegoats” (the Jews of Israel, of course). And the irony is that “some of Israel’s American political allies”—the Christian Right, if I understand correctly—“tend to deny the reality of climate change,” which, along with many other peculiarities, makes apocalypse more likely.

After reading this chapter and seeing its ritualistic homilies and sweeping comparisons, I became concerned that somehow I had been wrong about the intelligence, vision and insight that had characterized the rest of the book. But no, I am not wrong. Just skip the warning.