The purpose of this book is to present a generative theory of shape that significantly increases the power of geometry in the computational and design disciplines, as well as the physical sciences. This is achieved by requiring the generative theory to satisfy the following two criteria which we will regard as fundamental to intelligent and insightful behavior: (1) Maximization of Transfer. Any agent is regarded as displaying intelligence and insight when it is able to transfer actions used in previous situations to new situations. The ability to transfer past solutions onto new problems is at the very core of what it means to have knowledge. Thus, in our generative theory of shape, the generative sequences must maximize transfer along those sequences.