In one painting, a military officer in a Dutch sitting room flirts with a laughing girl. In another, a woman at a window weighs pieces of silver. Vermeer’s paintings haunt us with their beauty and mystery—what stories lay behind these stunningly rendered moments? As Timothy Brook shows us, these pictures, which seem so intimate, actually offer a remarkable view of a rapidly expanding world. The dashing officer’s hat is of beaver fur from Canada, while the pieces of silver, mined in Peru, might be used to purchase the Chinese porcelain seen in other Vermeer paintings. Moving outward from Vermeer’s studio, Brook traces the web of trade that was spreading across the globe in the seventeenth century. The wharves of Holland , wrote a French visitor, were “an inventory of the possible.” Vermeer’s Hat shows just how rich this inventory was, and how the urge to acquire such things was refashioning the world more powerfully than we have yet understood.