This package lets you generate planar and spherical triangle meshes, compute finite element calculations for 1- and 2-dimensional flat and curved manifolds with associated basis function spaces, methods for lines and polygons, and transparent handling of coordinate reference systems and coordinate transformation, including sf and sp geometries. The core fmesher library code was originally part of the INLA package, and implements parts of "Triangulations and Applications" by Hjelle and Daehlen (2006) <doi:10.1007/3-540-33261-8>.