This project deals with discrete and continuous dynamical systems, a cornerstone of the interplay between mathematics and science, the so-called Applied Mathematics. The theory of dynamical systems studies the main features (invariant objects, complexity, bifurcations associated to a change in the parameters, etc) of processes that evolve in time. Here the name “time” is self-explanatory for continuous dynamical systems, but it can also denote a natural number that labels the iteration step of a discrete process (discrete dynamical systems). The variety of scientific issues that can be analysed under this paradigm is overwhelming: chemical kinetics, astrodynamics, design of space missions, spread of infectious diseases over complex populations, neurosciences, fractal geometries arising in natural sciences, tumoral cell growth, structured populations in ecology, just to name a few examples.