Domain decomposition methods are widely used for numerical simulations on parallel machines from tens to hundreds of thousands of cores. Contrary to direct methods, domain decomposition methods are naturally parallel. This book provides a detailed overview of the most popular domain decomposition methods for partial differential equations (PDEs), focusing on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems. This book is beneficial to those working in domain decomposition methods, parallel computing and iterative methods, particularly those who need to implement parallel solvers for PDEs, as well as to mechanical, civil and aeronautical engineers, environmental scientists, and physicists.