The Department of Mathematics of the Politecnico di Milano is hosting a PhD program in Mathematical Models and Methods in Engineering, aiming at training high level researchers in advanced areas of Applied Mathematics. The teaching activities include a broad range of possibilities designed for the PhD program. As a successful approach to practical applications depends on a deep understanding of real-world phenomena and knowledge of mathematical tools for their description and for design, both modelling and methodological aspects are included, courses are offered in the area of natural sciences, in variational, differential and stochastic models, in numerical analysis and simulation, in operations research and computational and algorithmic methods.