This is a book on coupling, the method of establishing properties of random variables and processes (or any random things) through a joint construction on a common probability space. Coupling is a general method relevant in all fields of probabilistic inquiry; however, the main thrust is towards characterizations, approximations, asymptotics, and simulation. The book also includes self-contained treatments of stationarity (Palm theory) and regeneration (classical, wide-sense, time-inhomogeneous, and taboo regeneration). Other topics discussed are perfect simulation (MCMC) and quasi-stationarity. Links are made to several fields such as quantum physics and nonlocality, self-similarity, exchangeability, relativity, and queueing theory. The book is organized in chapters as follows: 1. Random Variables; 2. Markov Chains and Random Walks; 3. Random Elements; 4. Stochastic Processes; 5. Shift-Coupling; 6. Markov Processes; 7. Transformation Coupling; 8. Stationarity, the Palm Dualities; 9. The Palm Dualities in Higher Dimensions; 10. Regeneration. The book should be of interest to students and researchers in probability, stochastic modelling, and mathematical statistics. It is written with a Ph.D. student in mind, and the first two chapters can be read at a master's level and even at an advanced undergraduate level. The book is mathematically self-contained, relying only on the measure-theoretic basics and on elementary Markov chain theory. Hermann Thorisson received his Ph.D. from the Department of Mathematics, University of Göteborg, in 1981. He worked at the University of Göteborg, at Chalmers University of Technology, and at Stanford University, until returning to his home country to become a research professor at the Science Institute, University of Iceland.