Such farcical episodes recur throughout Cliff’s account and add unexpected levity to what is otherwise a dismal record of greed, savagery and fanaticism, especially — but not exclusively — on the part of the European explorers. The Portuguese didn’t know that Hinduism, let alone Buddhism or Jainism, existed. For them, the world was starkly divided between Christianity and Islam. They knew about Jews, of course; they’d been steadily persecuting them with renewed vigor in the 1490s by forced conversion, expulsion and massacre, but to them, Judaism was merely a forerunner of Christianity, not a faith in its own right.

Cliff’s narrative covers a huge span of time. For once the term “epic” seems an understatement. Da Gama’s exploits alone demand such terms. His maiden voyage took two years and traversed an extraordinary 24,000 miles, all this in leaky wooden vessels battered by storms and riddled with scurvy, and it was only the first of his three pioneering voyages that together established little Portugal as a world power.

To provide the widest possible context, Cliff begins with the Prophet Muhammad and the rise of Islam in the early seventh century and concludes with the siege of Vienna in 1529 and the subsequent rise of Dutch maritime expansion. His account of early Islamic history is brisk and factual, but it has a somewhat potted feel, as does his chapter on the crusades, for all the horrific detail he provides. This is, after all, well-trodden turf. When he finally comes to Portugal and its succession of zealous, sinister and quite dotty monarchs, he is in his element, and his book really takes off. He has a novelist’s gift for depicting character. From the fabled Henry the Navigator who, despite his appellation, “never set foot on an oceangoing ship,” to Vasco da Gama himself, at once steely and quixotic, to formidable figures like Magellan and the brutal Afonso de Albuquerque, who terrorized his victims by threatening to build a fort out of their bones and nail their ears to the door, he brings 16th-­century Portugal in all its splendor and squalor pungently to life.

Cliff is good too at such mundane but intricate matters as shipbuilding, royal protocols and the hazards of trade, all of which he documents by well-chosen citations from travel accounts, official papers and personal correspondence. Rather surprisingly, however, he fails to bring the great 16th-century Portuguese poet Luís de Camões into his account (though he’s mentioned in the very full bibliography), even though Camões participated in later Portuguese expeditions and wrote his Virgilian-style epic “The Lusiads” in praise of da Gama.