An introduction to the physics of active matter

•We review some introductory features of active matter physics.•We show how to model growing microbial colonies.•We discuss the physics of self-motile systems.•We provide an introduction to the physics of active gels.

In these notes we provide an introductory description of the physics of active matter, focusing on theoretical aspects, and on some methods which are often used in the field. We discuss a selection of active systems, where activity comes from different microscopic sources (mainly self-replication, self-propulsion, non-thermal forces), and in all cases we focus on their statistical physics and emergent collective behaviour, which is often linked to underlying nonequilibrium phase transitions. We hope to convey the idea that this field is a fascinating growing area of research at the interphase between statistical, soft matter and biological physics, and that active matter systems can possess, in general, a much richer physics than their passive counterparts.