1. Introduction -- 2. Quantum scattering with a spherically symmetric potential -- 3. The variational method for the Schrodinger equation -- 4. The Hartree-Fock method -- 5. Density functional theory -- 6. Solving the Schrodinger equation in periodic solids -- 7. Classical statistical mechanics -- 8. Molecular dynamics simulations -- 9. Quantum molecular dynamics -- 10. The Monte Carlo method -- 11. Transfer matrix methods -- 12. Quantum Monte Carlo methods -- 13. Computational methods for lattice field theories -- 14. High performance computing and parallelism -- App. A. Numerical methods -- App. B. Random number generators