We give an exposition of the Planarity Theorem of Maskit. This gives a classification of finitely generated groups acting effectively properly discontinously by orientation-preserving homeomorphisms on a planar surface. One can also realise such groups as kleinian function groups. We also explain how one can give another proof of the planarity theorem using Dunwoody's theory of tracks.
Enseign. Math. 68 (2022) 1-24.