On the cover of Timothy Brook’s enthralling new book is a well-known painting by Jan Vermeer of a laughing young woman in yellow, seated at a table and bathed in sunlight which floods through a half-open window. Her hands cup a crystal glass, and she is flirting with a dashing officer in a red coat seated opposite her. He has his back towards us, his right arm akimbo, but the composition is dominated by the outsized, black beaver hat he wears, fashionably trimmed with ribbon. This hat, and the diamond-paned window against which it is framed, set the stage for Vermeer’s Hat. The minutely observed and meticulously executed details in Vermeer’s paintings, Brook suggests, offer us metaphorical ‘doors’ – apertures opening up, like that half-open window, towards a wider world. Such doors, proposes Brook, take us directly into the rapidly expanding seventeenth-century world of global exploration and trade. Objects interjected into Vermeer’s compositions draw the reader’s eye and mind towards vistas beyond the sitters in their quintessentially Dutch surroundings.