Where in the world, in time, in what social set and body might you stand the best chance of becoming an adventurer? Someone who pursues the scintillating and the dangerous not because he or she will starve if they don't, but for the sheer excitement of it, the showing off, the acclaim? I reckon Richard Halliburton had it easy: a Princeton man, in an America just waking up to its global power, but still admired. In a world being eased open by the aeroplane. In a society abounding in wealth, and completely addicted to the story in print.

Given the inclination and the right spirit, how could you go wrong? And so Halliburton became the greatest adventurer in history. As the 1920s began he struck out for the far East, via the Matterhorn, Gibraltar, Cairo and Kashmir. The result was a bestseller called The Royal Road to Romance, and grateful editors financed his exploits  swimming the Hellespont and the Panama canal, for example  for the next decade. Halliburton was paid for derring-do, and his stories syndicated to newspapers across America. Seven League Boots, a string of tales that seem impossibly tall until you are able to corroborate them on the internet, is published here in a new edition. It begins with a commission "to go anywhere in the world I wished, and write about whatever pleased me".

In taking up the offer, Halliburton projects a cartoonish heroism. Here is Indiana Jones, but with more chutzpah. While waiting to hire an elephant he can ride over the Alps, he flits over to the Soviet Union on a whim. He stumbles on a great scoop of the era, conducting the only interview with one of the Tsar's principal assassins, Peter Ermakov. He spends an afternoon with Madame Lenin before heading south to Arabia and attempting to infiltrate Mecca dressed as a Muslim. He fails, but manages to entice Abdul-Aziz, the first King of Saudi Arabia, to a four-hour audience in the middle of the desert. In an Ethiopia on the brink of Italian invasion he dines with emperor Haile Selassie, his wife, daughter and the crown prince. Returning to France, he takes his elephant, Elysabethe Dalrymple, from the zoo in the Bois de Boulogne. With her trainer he leads her through the streets of Paris in the middle of the night to a waiting train. From there they travel to Martigny in Switzerland, where Halliburton becomes Hannibal, riding his exotic mount over the Alps to Italy.

All of this is related in an irrepressible, Boy's Own prose style. There are plenty of history lessons, though none of them would pass academic muster. In Cuba, telling the story of the Merrimac, a collier sunk during the Spanish American war, he writes: "Flash! A gun roars at the water's edge, from an almost invisible Spanish picket boat. Flash! Flash! Viperish streaks of fire, straight at the Merrimac's rudder. Whir! Clang! A shell strikes steel. The Spanish gunners rush out from their shelters  Two volcanoes of flame burst from the two hillsides."

And though he's what would have been considered at the time gentle and fair, Halliburton is also an unthinking chauvinist. He is surprisingly nuanced (which isn't saying much) about the achievements of the Soviet system, but America is this Memphis boy's lodestar of civilisation. Traditional societies, black ones in particular, are "primitive". His retelling of the astonishing story of Henri Christophe, King of Haiti, is polluted with racist condescension and stereotype. But curiosity and a love of the unfamiliar also leap from the pages. Halliburton may have maintained a sense of his own people's natural superiority, but he chose to spend as much time as possible away from them, in the company of "Bolsheviks" and "Mohammedans" alike.

He was estranged in another way, too. This Indiana Jones was gay, it seems. That is the conclusion biographers have come to, in the absence of any definitive evidence. His boyfriends are said to have included the silent film star Ramón Novarro and the writer Paul Mooney. Mooney accompanied Halliburton on his last voyage in 1939, just four years after Seven League Boots was published. They were both lost at sea in a Chinese Junk, their adventure truncated.

Halliburton's writing has none of the camp and old-world irony of Robert Byron, who was writing about some of the same places at the same time. Instead he offers a glimpse of a long-lost, wide-eyed America. Rewritten for children and packaged as the "Book of Marvels", his stories embedded themselves in the minds of an entire generation. A second-hand copy easily enchanted me as a child. "I'm grown up now," he writes in the introduction. "But as yet I haven't any son or any daughter to go traveling with me. And so, in their places, may I take you?"

Who could resist the invitation?