When maps aren’t simply telling you how to get from here to there, they make political statements, lay out the terrain of history, show you the landscape of the imagination,  play games—and always look beautiful. The Curious Map Book (Chicago, $45) is a showcase of such “cartographic curiosities.” Assembled by Ashley Baynton-Williams, a British antiquarian map dealer, the survey starts with a 1493 world map that’s also a chart of Western humanism, depicting the Earth divided in four parts, one for each of Noah’s sons, with side trips into medieval legend and classical myth. A 1518 rendering of Utopia depicts the island with a death’s head: map as memento mori. In human shape, maps were allegories and caricatures; as animals, they united disparate regions into the body of a fierce lion or warned of grasping imperial ambitions, showing Russia in 1877 as an octopus. Other maps chart the course of love, and many play games. The first board games, circa 1588, were maps, with players throwing dice and racing each other around a hemisphere. Some required gambling, others doubled as Trivial Pursuit, requiring players to recite facts about the regions they landed on. Maps became jigsaw puzzles in the 18th century, and one impressive picture here shows a stunning 1866 globe jigsaw. A tribute to human wit and ingenuity, these selections have an illuminating and unobtrusive guide in Baynton-Williams, whose succinct commentary profiles the mapmakers and explains their methods and materials.