This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. The authors carefully explain the relationship between domain decomposition and multigrid methods at an elementary level, and they discuss the implementation of domain decomposition methods on massively parallel supercomputers. They fully describe and explain all algorithms and carefully develop a mathematical framework for the analysis and complete understanding of the methods. In addition, they include numerous numerical examples to demonstrate the behavior of this important class of numerical methods.