Potential theory describes the behavior of gravitational, magnetic, and fluid potentials. This introductory-level book covers the classical three-dimensional Euclidean setting involving the Laplacian and its surface counterpart based on the Beltrami operator. This approach provides a connecting link between two areas of geomathematical research: the exterior of the earth and the earth's surface in its spherical manifestation. The text discusses the approximation of gravitational potential from gravity measurement, the separation of the magnetic field into interior and exterior, and ionspheric current systems from magnetic field measurements.