This lecture is part of an online graduate course on Lie groups.
We give a sketch of the Bianchi classification of the Lie algebras and groups of dimension at most 3. We mention that this is related to the Thurston geometries of 3-manifolds.
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53RWBkiHKoOsTw-dGHAoJ-h
