This appendix develops systematic methods for solving electrostatic boundary value problems with spherical symmetry. Starting from Laplace’s equation in spherical coordinates, it separates variables to obtain radial solutions and angular solutions given by the spherical harmonics Ylm. It then constructs generating functions for Ylm, explains why the degeneracy factor 2l + 1 arises so often, and reviews azimuthally symmetric solutions in terms of Legendre polynomials and their completeness and orthogonality. The Coulomb Green’s function with a point source at an arbitrary location is expanded in spherical harmonics, illustrating how to build free-space and image-charge Green’s functions adapted to spherical geometries. The appendix also derives the spherical-harmonic expansion of a plane wave and shows how to use it in scattering and radiation problems. Finally, it develops a multipole expansion for the interaction energy between a localized charge distribution and an external potential, expressing the result in terms of spherical multipole moments and their couplings.