"What shape is space?" is a question with surprisingly far-reaching implications for our understanding of the very nature of reality and our place within it. The concepts involved may be sophisticated, but Giles Sparrow's effortless prose style easily renders them understandable, allowing readers to get to grips with the overarching debates at the cutting edge of cosmology today. Infographics, diagrams and astronomical visualizations illustrate and clarify the various astonishing implications of a universe of infinite space.