I presented a general introduction to domain decomposition methods structured into four parts: 1) Classical Schwarz methods 2) Dirichlet-Neumann, Neumann-Neumann and Optimized Schwarz Methods 3) Waveform relaxation variants of the above methods and preconditioning 4) Scalability and coarse space corrections In each part, I gave a historical introduction, showed mathematically what convergence behavior the methods have, and also gave numerical illustrations.