This book is a systematic introduction to the new and rapidly evolving field of patterns in granular materials. Granular matter is usually defined as a collection of discrete macroscopic solid particles (grains) with a typical size large enough that thermal fluctuations are negligible. Despite this seeming simplicity, properties of granular materials set them apart from conventional solids, liquids, and gases due to the dissipative and highly nonlinear nature of forces among grains. The last decade has seen an explosion of interest to nonequilibrium phenomena in granular matter among physicists, both on experimental and theoretical sides. Among these phenomena, one of the most intriguing is the ability of granular matter upon mechanical excitation to form highly ordered patterns of collective motion, such as ripples, avalanches, waves, or bands of segregated materials. This book combines a review of experiments with exposition of theoretical concepts and models introduced to understand the mechanisms of pattern formation in granular materials. The unique feature of this book is a strong effort to extend concepts and ideas developed in granular physics beyond the traditionally defined boundaries of the granular physics towards emergent fields, especially in biology, such as cytoskeleton dynamics, molecular motors transport, ordering of cells and other active (self-propelled) particles, dynamic self-assembly, etc.