Lie Sphere Geometry in $\mathbf R^3$
These notes introduce Lie sphere geometry of surfaces in Euclidean 3-space. A similar article with a different point of view is: G. R. Jensen, Dupin hypersurfaces in Lie sphere geometry, in: Geometry and Analysis on Manifolds, Progr. Math. 308, Birkhäuser/Springer, Cham, 2015, 383–394. More details are in the book: G. R. Jensen, E. Musso, L. Nicolodi, Surfaces in Classical Geometries, Universitext, Springer, Cham, 2016, Chapter 15. An exposition of Lie sphere geometry in all dimensions is in: Th. E. Cecil, Lie Sphere Geometry, Universitext, Springer, New York, 2008.