I. Numerical Methods.- Error Analysis.- Interpolation.- Numerical Differentiation.- Numerical Integration.- Systems of Inhomogeneous Linear Equations.- Roots and Extremal Points.- Fourier Transformation.- Wavelets.- Random Numbers and Monte Carlo Methods.- Eigenvalue Problems.- Data Fitting.- Discretization of Differential Equations.- Equations of Motion.- II. Simulation of Classical and Quantum Systems.- Rotational Motion.- Molecular Mechanics.- Continuum Mechanics.- Thermodynamic Systems.- Random Walk and Brownian Motion.- Electrostatics.- Waves.- Diffusion.- Convection.- Nonlinear Systems.- Simple Quantum Systems.- Quantum Many -Body Systems.