A friendly and systematic introduction to the theory and applications. The book begins with the sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments, which are
later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies to randomly stopped processes and unbiased estimation. The authors then proceed with the theory of decoupling in full
generality, paying special attention to comparison and interplay between martingale and decoupling theory, and to applications. These include limit theorems, moment and exponential inequalities for martingales and more general
dependence structures, biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. Addressed to researchers in probability and statistics and to graduates, the expositon 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.