The chapter "Potential Theory in Gravity and Magnetic Applications" by Richard J. Blakely provides a comprehensive overview of potential theory and its applications in gravity and magnetic fields. The introduction covers the basics of potential fields, energy, work, and harmonic functions, including Laplace's equation and complex harmonic functions. It also discusses Green's identities, Helmholtz theorem, and Green's functions. The subsequent sections delve into the Newtonian potential, detailing gravitational attraction and the potential of mass distributions, such as spherical shells and solid spheres. The chapter also explores magnetic potential, including magnetic induction, Gauss's law for magnetic fields, vector and scalar potentials, and dipole moments. It covers magnetization, magnetic field intensity, and Poisson's relation, with examples for spheres, slabs, and cylinders. Spherical harmonic analysis is introduced, covering zonal and surface harmonics, and their application to Laplace's equation. The chapter then discusses regional gravity fields, including gravity anomalies and corrections, and the geomagnetic field, its components, and crustal magnetic anomalies. Forward and inverse methods are covered, including gravity and magnetic models, and the determination of source properties. Fourier-domain modeling is discussed, including Fourier transforms, random functions, and Earth filters. The chapter concludes with transformations, such as upward continuation, directional derivatives, phase transformations, and horizontal gradients, along with a review of vector calculus, subroutines, sampling theory, and unit conversion.The chapter "Potential Theory in Gravity and Magnetic Applications" by Richard J. Blakely provides a comprehensive overview of potential theory and its applications in gravity and magnetic fields. The introduction covers the basics of potential fields, energy, work, and harmonic functions, including Laplace's equation and complex harmonic functions. It also discusses Green's identities, Helmholtz theorem, and Green's functions. The subsequent sections delve into the Newtonian potential, detailing gravitational attraction and the potential of mass distributions, such as spherical shells and solid spheres. The chapter also explores magnetic potential, including magnetic induction, Gauss's law for magnetic fields, vector and scalar potentials, and dipole moments. It covers magnetization, magnetic field intensity, and Poisson's relation, with examples for spheres, slabs, and cylinders. Spherical harmonic analysis is introduced, covering zonal and surface harmonics, and their application to Laplace's equation. The chapter then discusses regional gravity fields, including gravity anomalies and corrections, and the geomagnetic field, its components, and crustal magnetic anomalies. Forward and inverse methods are covered, including gravity and magnetic models, and the determination of source properties. Fourier-domain modeling is discussed, including Fourier transforms, random functions, and Earth filters. The chapter concludes with transformations, such as upward continuation, directional derivatives, phase transformations, and horizontal gradients, along with a review of vector calculus, subroutines, sampling theory, and unit conversion.