The Physics of the Vicsek model

In these lecture notes, prepared for the Microswimmers Summer School 2015 at Forschungszentrum Julich, I discuss the well known Vicsek model for collective motion and its main properties. In particular, I discuss its algorithmic implementation and the basic properties of its universality class. I present results from numerical simulations and insist on the role played by symmetries and conservation laws. Analytical arguments are presented in an accessible and simplified way, but ample references are given for more advanced readings.