4. Imperial Politics: Kwon Kun's Kangnido Map (1402)

What's most striking about this Korean map, designed by a team of royal astronomers led by Kwon Kun, is that north is at top. "It's strange because the first map that looks recognizable to us as a Western map is a map from Korea in 1402," Brotton notes. He chalks this up to power politics in the region at the time. "In South Asian and Chinese imperial ideology, you look up northwards in respect to the emperor, and the emperor looks south to his subjects," Brotton explains. Europe is a "tiny, barbaric speck" in the upper left, with a circumnavigable Africa below (it's unclear whether the dark shading in the middle of Africa represents a lake or a desert). The Arabian Peninsula is to Africa's right, and India is barely visible. China is the gigantic blob at the center of the map, with Korea, looking disproportionately large, to its right and the island of Japan in the bottom right.

5. Territorial Exploration: Waldseemuller's Universalis Cosmographia (1507)

This work by the German cartographer Martin Waldseemuller is considered the most expensive map in the world because, as Brotton notes, it is "America's birth certificate"—a distinction that prompted the Library of Congress to buy it from a German prince for $10 million. It is the first map to recognize the Pacific Ocean and the separate continent of "America," which Waldseemuller named in honor of the then-still-living Amerigo Vespucci, who identified the Americas as a distinct landmass (Vespucci and Ptolemy appear at the top of the map). The map consists of 12 woodcuts and incorporates many of the latest discoveries by European explorers (you get the sense that the woodcutter was asked at the last minute to make room for the Cape of Good Hope). "This is the moment when the world goes bang, and all these discoveries are made over a short period of time," Brotton says.

6. Politicized Geography: Ribeiro's World Map (1529)

The Portuguese cartographer Diogo Ribeiro composed this map amid a bitter dispute between Spain and Portugal over the Moluccas, an island chain in present-day Indonesia and hub for the spice trade (in 1494, the two countries had signed a treaty dividing the world's newly discovered lands in two). After Ferdinand Magellan's expedition circumnavigated the globe for the first time in 1522, Ribeiro, working for the Spanish crown, placed the "Spice Islands," inaccurately, just inside the Spanish half of his seemingly scientific world maps. Ribeiro may have known that the islands (which appear on the far-left and far-right sides of the map) actually belonged to Portugal, but he also knew who paid the bills. "This is the first great example of politics manipulating geography," Brotton says.

7. Territorial Navigation: Mercator's World Map (1569)

Next to Ptolemy, Brotton says, Gerardus Mercator is the most influential figure in the history of mapmaking. The Flemish-German cartographer tried "on a flat piece of paper to mimic the curvature of the earth’s surface," permitting "him to draw a straight line from, say, Lisbon to the West Coast of the States and maintain an active line of bearing." Mercator, who was imprisoned by Catholic authorities for alleged Lutheran heresy, designed his map for European navigators. But Brotton thinks it had a higher purpose as well. "I think it’s a map about stoicism and transcendence," he says. "If you look at the world from several thousands miles up, at all these conflicts in religious and political life, you’re like ants running around." Mercator has been accused of Eurocentrism, since his projection, which is still occasionally used today, increasingly distorts territory as you go further north and south from the equator. Brotton dismisses this view, arguing that Europe isn't even at the center of the map.