The elements of geometry are points, lines and planes, together with Space and Nothing. In Euclidean geometry, we observe these as if we are point-centered beings concerned with extensive measurement. In non-Euclidean, or projective geometry, we are ‘planar’ beings observing spatial relations, free of measurement, as dynamic and transformational. According to the author, this is a polar opposite vision of intensive space, and it reveals remarkable secrets. Edwards invites the reader to discover these secrets through practical exercises in creative geometry.