The course offers an introduction to Dynamical Systems from an applied and practical point of view. It will offer students the opportunity to learn how to compute the behaviour of differential equations as parameters varies. Topics include: linear  dynamical systems and their stability, Routh-Hurwitz conditions, autonomous Systems, non-linear dynamical systems, equilibrium points and their stability, almost linear systems, phase plane analysis: direction fields and phase portraits, Lyapunov stability (simple and damped pendulum), periodic solutions, limit cycles, bifurcation  theory, chaos and attractions.