Introduction Numerical methods in chemical engineering deal with a broad range of problems starting from calculations on atomic or molecular level to the optimization of complete chemical plants. From an engineer's point of view, we will expound the following subjects: -- quantum mechanical calculations of atoms and molecules -- numerical treatment of chemical reaction kinetics -- transport processes -- mathematical description of unit operations -- stationary and instationary simulation and optimization of chemical plants Because of this extensive field we will have to refer to other overview papers. Quantum mechanics of atoms and molecules, Monte Carlo and Molecular Dynamics Methods Exact solutions for many-electron systems are essentially unattainable, except for some trivial cases, since an exact solution would imply an exact Hamiltonian, which is unavailable. In practice model