Phyllotaxis, the study of the patterns determined by leaves, petals, and other organs of plants, raises some of the deepest questions of plant morphogenesis. What principles of biological organisation produce these dynamical geometric systems? The constant occurrence of the Fibonacci sequence in such systems is a phenomenon that has fascinated botanists and mathematicians for centuries. In this book, the many facets of phyllotaxis are dealt with in an integrated manner for the first time. The author describes a unified concept of phyllotaxis, and presents a mathematical model of plant growth based on experimental, anatomical, cellular, physiological and palaeontological observations. The model not only provides a framework for formal analyses of botanical data, but also emphasises the relevance of phyllotaxis to other structures, such as crystals and proteins, making this book of interest to crystallographers and physicists as well as to botanists and mathematicians.