Inserted: 5 jan 2018
Last Updated: 22 oct 2018
Journal: to appear on Springer INdAM Series
These are notes of a course given at the INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics", organized by Serena Dipierro at the University of Bari, from April to June 2017.
We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.