Thornton sets out to unsettle a collective memory of the Americas that still runs in one direction, from Europe outward. His remedy is Atlantic history practised less as heritage-keeping or moral judgement than as social science: societies are set beside one another because the comparison is analytically useful, not because one of them is ours.

The opening pages take up early European voyaging, then treat Europe, Africa and the American continents in turn, comparing political forms as far apart as those of the Iroquois and the Tupi. A middle section sorts expansion into three kinds of encounter, conquest, colonization and contact, which lets in regions normally dropped from such accounts: the American West, the western Caribbean, Atlantic Africa itself, places where Europeans arrived as guests or were thrown out.

Culture comes late and stays comparative, taking up the survival and loss of languages, virtuosity in aesthetic forms, and revelation in religion.