This course presents two complementary methodologies for experimental studies: dimensional analysis and design of experiments. Dimensional analysis relies on the determination of non-dimensional numbers (also called pi-terms) based either on physical equations or on dimensional equations. The remaining experimental space can therefore been studied more easily, but this requires its exploration with a methodology: how many experiments? which experiments? how many repetitions? how to model the data? is this model fitting the data correctly? is it significant with respect to the experimental noise? These are some of the questions studied in the design of experiments methodology. We will include factorial and fractional designs, composite designs and introduce optimality criteria to design optimal designs.