This course is aimed at junior/senior undergraduate and graduate students interested on the numerical description of the equilibrium and kinetics of materials. The focus will be on systems that are conceived at the nanoscale and whose resultant properties and performance have an impact on the associated mesoscopic and macroscopic length scales. By starting from real-life example applications, students will be exposed to advantages and disadvantages of phase field, sharp, and level set microstructural evolution methods. Associated numerical techniques such as finite differences, finite elements, and finite volumes will be reviewed. Practical aspects associated to modeling of materials, such as model validation, data fitting, links and incorporation of mesocontinuum models, optimal meshing criteria, and model convergence and stability are very important aspects of the class. Example applications include prediction of phase diagrams, intercalation kinetics in rechargeable lithium-ion batteries, electromigration, domain switching in ferroelectric random access memories, spinodal decomposition, and single-component solidification. The class meets two times a week, and for each classroom (theory) lecture a computer lab lecture will be held, making it a very hands-on course.