1. An introduction to the Method of Lines (MOL); 2. A one-dimensional, linear partial differential equation; 3. Green’s function analysis; 4. Two nonlinear, variable coeffcient, inhomogeneous PDEs; 5. Euler, Navier-Stokes and Burgers equations; 6. The Cubic Schrödinger Equation (CSE); 7. The Korteweg-deVries (KdV) equation; 8. The linear wave equation; 9. Maxwell’s equations; 10. Elliptic PDEs: Laplace's equation; 11. Three-dimensional PDE; 12. PDE with a mixed partial derivative; 13. Simultaneous, nonlinear, 2D PDEs in cylindrical coordinates; 14. Diffusion equation in spherical coordinates; Appendix 1: partial differential equations from conservation principles: the anisotropic diffusion equation; Appendix 2: order conditions for finite difference approximations; Appendix 3: analytical solution of nonlinear, traveling wave partial differential equations; Appendix 4: implementation of time varying boundary conditions; Appendix 5: the DSS library; Appendix 6: animating simulation results.