Introduction -- Preparation Knowledge of Material Properties -- Preparation Knowledge of Classical Mechanics -- Preparation Knowledge of Numerical Analysis -- General Finite Element Methods with Special Focusing on XFEM -- General Finite Element Methods with Special Focusing on NMM -- Discrete Element Methods with Special Focusing on DEM -- Discrete Element Methods with Special Focusing on DDA -- Mesh-free Methods with Special Focusing on EFGM -- Mesh-free Methods with Special Focusing on SPH -- Hybrid Methods with Special Focusing on DEM-SPH.