The purpose of this book is to encourage mathematicans to illustrate their work and to help artists understand the abstract ideas expressed by such drawings. It explains the graphic design of illustrations from Thurston's world of low-dimensional geometry and topology, while presenting the principles of linear and aerial perspective from the viewpoint of projective and descriptive geometry. "Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what `hands on' really means." -- John Stillwell, University of San Francisco