Although pattern and image analysis have their conceptual foundations in the mathematical sciences, it is now applied widely in many other areas of science. It embodies the techniques used to evaluate and compare the patterns, shapes, and other images -- natural and artificial -- that may range from such electronic forms as CAT scans and satellite images to patterns as ancient as the non-random assembly of letters that comprise a language. In Patterns Ulf Grenander has written a book both for the student of mathematics and for the specialist who works with patterns in other fields, such as biology and medicine. Grenander begins by examining the nature of patterns and what distinguishes them from randomness. He then provides the mathematical foundation for the concepts and phenomena introduced. Finally, he provides examples and demonstrations of computer algorithms that permit the reader to recreate and explore some of the patterns discussed in the book. "A dazzling tour de force on patterns. It is a substantial, original contribution by a leader -- indeed, originator -- in the field, and has the potential for significant impact on the direction of future research. It includes a profoundly insightful treatise on patterns, their nature, and the role of randomness in generating and analyzing them. Examples range from language to weaving to cellular biology. Even non-statisticians and non-scientists reading this material will find their thoughts clarified and provoked." -- Alan F. Karr, National Institute of Statistical Sciences