We give an elementary introduction to Rauzy-Veech induction on the space of interval exchange transformations (IETs). We illustrate its „renormalization“ mechanism using simple examples and discuss its relationship with the Teichmüller geodesic flow. We introduce some important notions related to the induction, such as a combinatorial rotation number as well as towers over an IET, and discuss some of the key results proved using Rauzy-Veech induction. We conclude by explaining why, also in todays research, it remains a widely used and powerful tool.
