The second edition of this textbook has been substantially enlarged. It now includes a chapter on catastrophe theory and bifurcation, which bring these recently developed techniques within the range of the geographer; and allows for a considerable increase in the number of exercises and worked examples. These are provided to help the student master the mathematics and to relate mathematical methods to geographical problems. The examples are taken from recent literature and from the classical models of von Thunen, Weber and others. Geographical statisticians; spatial analysts; students of planning.