“It was an obscure word, ‘appertaining,’” Immerwahr writes, “as if the law’s writers were mumbling their way through the important bit.” It seemed to signal a discomfort, or at least the semblance of it. Soon enough, such official compunction was decidedly on the wane. Theodore Roosevelt, serving as William McKinley’s assistant secretary of the navy, pursued the Spanish-American War of 1898 with the zeal you would expect of someone who toted around a book called “Anglo-Saxon Superiority.”

Immerwahr devotes several chapters to the ensuing five decades, as the United States annexed Puerto Rico and the Philippines, brutally crushing independence movements, torturing Filipino insurgents with “the water cure” and giving mainland doctors veritable carte blanche to treat Puerto Rico as a medical laboratory. Seen through Immerwahr’s lens, even the most familiar historical events can take on a startling cast. Take World War II in the Philippines: Pointing to the murderous combination of American shelling and Japanese slaughter of civilians, he calls the war “by far the most destructive event ever to take place on U.S. soil.”

The role that racism played in the country’s colonial acquisitions was palpable but sometimes counterintuitive. While imperialists often spoke about “civilizing” the “savages,” some of the most ardent anti-imperialists in the 19th century were white supremacists like John C. Calhoun, the senator from South Carolina, who was wary of letting “any but the Caucasian race” into the Union. The 1867 purchase of Alaska from the Russians encountered similar resistance, with The Nation complaining about the prospect of “Exquimaux fellow citizens.” As Immerwahr tartly observes, “The deal went through only because, in the end, there weren’t that many ‘Exquimaux,’ and there was quite a lot of Alaska.”

Immerwahr brings the narrative up to the present day, exploring the American decision to give up territory after World War II, which he calls “virtually unprecedented” — after all, victorious countries tended to do the opposite. But this “twilight of formal empire” wasn’t simply the result of American selflessness. Technological advances eroded the connection between power and land. Securing access to a raw material like rubber mattered less when you could manufacture a synthetic version of it. The big exception, of course, has been oil — “the one raw material that has most reliably tempted politicians back into the old logic of empire.”

What the United States has now is a “pointillist empire”: specks of land scattered around the world that have served as military bases, staging grounds, detention facilities, torture sites. (The United States has 800 overseas bases, whereas Russia has nine; most countries have zero.) If Theodore Roosevelt was the swashbuckling emblem of the country’s formal empire, Herbert Hoover — “an astonishingly capable bureaucrat” before he became a not-very-capable president — represented the turn toward globalization, standardization and logistics.

It’s a testament to Immerwahr’s considerable storytelling skills that I found myself riveted by his sections on Hoover’s quest for standardized screw threads, wondering what might happen next. But beyond its collection of anecdotes and arcana, this humane book offers something bigger and more profound. “How to Hide an Empire” nimbly combines breadth and sweep with fine-grained attention to detail. The result is a provocative and absorbing history of the United States — “not as it appears in its fantasies, but as it actually is.”