The field of Dynamical Systems covers a huge set of mathematical theories and techniques. Its primary goal is to model phenomena that evolve with time and as such, Dynamical Systems are of common use in applications, see here. From a mathematical point of view, it basically starts with ordinary differential equations in which only a variable, typically the time is considered. But Dynamical Systems include much more as equations describing time evolution may also include space, stochastic terms, discrete or continuous models... From chaos theory to fluid dynamics, from complex systems to quantum mechanics, from epidemics to neuroscience, mathematical equations describing the evolutions of specific quantities of interest have been --are and will be-- at the heart of science development and the increase of knowledge.