This course is intended to give a deeper understanding of basic physical and chemical processes that are important in petrology. The students will learn how to describe physical-chemical processes such as heat flow, diffusion, reaction, deformation and fluid flow by mathematical means. They will learn how the processes are strongly relying on thermodynamic principles, and how they are coupled to each other as they are in nature. During the course we will combine theoretical understanding with practical applications by mixing the derivation of equations with the actual usage of them in simple numerical simulations. The students will advance their skills in mathematics using symbolic math software to derive equations, as well as (further) develop numerical modelling skills using MATLAB, Octave or Python. In the end they will be able to simulate some coupled physical-chemical processes such as reactive-fluid flow processes, phase growth modelling and diffusion, rock deformation coupled with reaction, or any other processes of the students’ interest. Most importantly they will understand where the equations that govern the complex petrological processes come from. They will have an understanding of what classical irreversible thermodynamics is about and how to use this to develop it further in their own research.