This book explores a wide range of mathematical concepts relating to regularly repeating surface decoration and provides a comprehensive means of classifying patterns and tilings. It covers issues from basic concepts of symmetry to more complex issues such as graph theory, group theory, and topology. The author elaborately illustrates the concepts, thereby rendering this complex area-previously best understood by mathematicians and crystallographers-accessible to artists and designers. Although it focuses principally on the characteristics of surface-pattern designs, the material addresses all types of surface designs, including textiles, wallpapers, and building and wrapping materials. This book is an extremely valuable guide for textile designers, artists, designers, architects, and anyone interested in the geometric aspects and applications of surface designs, patterns, and tilings.