Ikelle, L.T., 2011. Review: Coordinate transformation of acoustic and Maxwell’s equations: The making of anisotropic mass density and permittivity. Journal of Seismic Exploration, 20: 207-216. It is a remarkable fact that Maxwell’s equations under any coordinate transformation can be written in an identical mathematical form as the ones in Cartesian coordinates. However, in some particular coordinate transformations, like the cylindrical coordinate transformations, the physical properties become anisotropic, even if they are isotropic in the Cartesian coordinates. Even the permittivity can be anisotropic. The remarkable invariance of Maxwell’s equations under coordinate transformation extend to acoustic wave equations. In other words, the acoustic wave equations are also invariant under any coordinate transformation. However, the mass density can become anisotropic. We here review these fundamental results.