Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. It was born in the early 1980s as a natural continuation of martingale theory and has acquired a life of its own due to vigorous development and wide applicability. The authors provide a friendly and systematic introduction to the theory and applications of decoupling. This book is addressed to researchers and graduate students in probability and statistics. The exposition is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course.