Assuming only a minimal prerequisite math training (simple linear algebra and its derivatives), the author provides a solid grounding in basic mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing numerical methods and modeling key. 8 are well documented, state-of-the-art visco-elasto-plastic, 2-D model is then presented, which enables robust modeling of key dynamic processes such as subduction, lithospheric extension, collision, slab break-off, intrusion emplacement , mantle convection and the formation of the planet's core.