Americans have quaint delusions that they are anti-imperialist, though they created on their own continent the greatest empire in history. David Reynolds takes his title from Thomas Jefferson's line about building “an empire of liberty”. The belief that actions deemed aggressive, expansionist or oppressive by other nations become acceptable if undertaken by a people with such high purposes as those asserted by Americans persists into George Bush's 2004 line: “We're not an imperial power. We are a liberating power.”

George Washington wrote without irony on the eve of the great independence struggle in 1774: “The crisis is arrived when we must assert our rights, or submit to every imposition that can be heaped upon us till custom and use will make us as tame and abject slaves as the blacks we rule over with such arbitrary sway.”

David Reynolds, Professor of International History at Cambridge, probably knows more about America than any other British writer. He is the author of In Command of History, an exemplary study of Churchill as war leader and war memoir-writer. His latest book is linked to his current BBC radio series. It would be mistaken, however, to see this merely as a tie-in work. Reynolds has done a masterly job on the radio, but his book is even better, providing a panoramic political and social history of America from earliest times to Barack Obama.

His admiration for American achievement is undiminished by the clear-sightedness with which he dispels its historical myths, chronicles its failures and remarks on its ruthlessness. America created an empire mostly by war: against France, Spain, Britain, Mexico and above all the wretched “Indians” that the white newcomers dispossessed.

White immigrants, though, did not occupy an empty land: archeological evidence suggests that some native American communities in the 11th century were remarkably advanced builders. From the 17th century onwards, the new Americans slaughtered the old ones wholesale, first by infecting them with plagues against which they possessed no immunity, then in the course of expansionist wars.

Reynolds records the exhilaration of a colonist arriving from Inverness in the 1770s: “The price of land is so low...that 40 or 50 pounds will purchase as much ground as one thousand in this country...There are few or no taxes at present...The climate in general is very healthy...Lastly, there are no titled, proud lords to tyrannise over the lower sort of people, men there being upon a level and more valued in proportion to their abilities than they are in Scotland.”

Contrast this euphoria with the unspeakable misery of John Ross, chief of the Cherokees (his name came from his Scottish father), whose people were herded west across the Mississippi in the late 1830s, dying in their hundreds, to make way for land-hungry settlers. Ever since white men arrived in America, wrote Ross, “we have been made to drink of the bitter cup of humiliation; treated like dogs; our lives, our liberties, the sport of the white men; our country and the graves of our Fathers torn from us”.

Beyond the native Americans, there were also, of course, a multitude of shackled blacks. Both Washington and Jefferson owned slaves, who accounted for 700,000 of the 3.9m population of the new United States in 1790. The most costly conflict in the nation's history - more people died in the 1860s civil war than America lost in the two 20th-century global struggles put together - was fought over slavery.

Yet a century on, as Reynolds vividly describes, a civil-rights struggle had to be fought, to make black Americans truly free and end racial segregation. Lyndon Johnson is today chiefly remembered as the president who “escalated” America's disastrous Vietnam war. Yet he deserves recognition instead as the unlikely Texan who made black American freedom a reality.

The people of the New World have always possessed startling self-confidence, exemplified by New York editor John L Sullivan, who in 1845 looked forward a century to “the 250 or 300 millions - and American millions - destined to gather together beneath the fluttering stripes and stars in the fast-hastening year of the Lord 1945”. Sullivan denounced British efforts to thwart American expansion, “checking the fulfilment of our manifest destiny to overspread the continent allotted by providence for the free development of our yearly multiplying millions”.

America acquired space relentlessly, by migration westwards and by purchase: of Louisiana from France in 1803 when Napoleon needed hard cash to fund his invasion of England; of New Mexico and California from Mexico for $15m in 1848; of Alaska from Russia in 1867 for $7.2m. Many Americans thought this a lousy deal. As late as the 1950s, when there was talk of oil in the frozen wastes, a senior executive scoffed that it would cost $5 a barrel to extract, “and oil will never get to $5 a barrel in our lifetime”.

Part of the pleasure in Reynolds's book are its moments of serendipity. He handles the big political set pieces superbly, but also offers many whimsical vignettes. For instance, the American depression of the 1890s prompted a wave of xenophobia towards immigrants, and a choleric New York newspaper editorial: “The floodgates are open. The bars are down. The sally-ports unguarded. The dam is washed away. The sewer is choked...The scum of immigration is viscerating upon our shores. The horde of $9.60 steerage slime is being siphoned upon us from Continental mud tanks.”

I had never heard of Bill and Alfred Levitt, who in the 1950s did for American suburban housing what Henry Ford achieved for motoring a generation earlier with his model T. The Levitts offered two standard designs - a four-room Cape Cod box and a single-storey ranch house, each with a free Bendix washing machine thrown in, at prices millions could afford, in new garden communities with curved streets and no fences. In those Red-fixated times, Bill Levitt said: “No man who owns his own house and lot can be a communist. He has too much to do.”

In Reynolds's book, you will also find the tale of the late 19th-century railroad boom; of Henry Heinz and his canned beans; the fact that 134 British peers sold coronets for cash in marriage to American heiresses between 1870 and 1914; and details of that dazzling engineering achievement completed in 1825, the 363-mile Erie Canal that opened navigation from the Great Lakes to the sea. The canal rose 600ft from the Hudson river through its chain of 83 locks.

It is a brave but mildly perilous undertaking to carry the story right through the Iraq war to Obama's inauguration. Journalism takes over from history in the last pages of the book. But that is a quibble. Reynolds declares as his theme: “It makes sense to see the United States in a continuum with earlier imperial powers, rather than to accept the doctrines of American exceptionalism - the idea that the United States is both historically unique and morally exemplary.” He carries this to a triumphant conclusion.

The author stands beside Simon Schama as a populariser of history whose work also represents the widest knowledge and highest scholarship. This is the best single-volume account of the world's greatest society for many years. Even those of us who think we know America well are reminded anew what an awesome place it is, even if its record is a trifle less noble than its citizens like to think.

America, Empire of Liberty by David Reynolds
Allen Lane £30 pp704

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