Michael Leyton has developed new foundations for geometry in which shape is equivalent to memory storage. A principal argument of these foundations is that artworks are maximal memory stores. The theory of geometry is developed from Leyton's fundamental laws of memory storage, and this book shows that these laws determine the structure of paintings. Furthermore, the book demonstrates that the emotion expressed by a painting is actually the memory extracted by the laws. Therefore, the laws of memory storage allow the systematic and rigorous mapping not only of the compositional structure of a painting, but also of its emotional expression. The argument is supported by detailed analyses of paintings by Picasso, Raphael, Cezanne, Gauguin, Modigliani, Ingres, De Kooning, Memling, Balthus and Holbein.