The elements of geometry are points, lines and planes, together with Space and Nothing. In Euclidian geometry, we observe these as if we are point-centred beings concerned with extensive measurement. In non-Euclidian, or projective geometry, we are 'planar' beings observing spatial relations, free of measurement, as dynamic and transformational. This polar opposite vision of intensive space reveals remarkable secrets. In this fascinating and useful book, expert Lawrence Edwards invites the reader to discover these secrets through practical exercises in creative geometry. Topics include: the elements of geometry, duality, collineation, cross ratio, the circling and step measure, conics and the nature of a curve.