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"Multipole expansions" as a book category covers the mathematical methods and physical intuitions for representing spatially distributed fields and potentials by sums of simpler, spatially separated contributions (monopole, dipole, quadrupole, etc.). Titles in this category range from introductory treatments that develop Legendre polynomials, spherical harmonics and the basic expansion of electrostatic or gravitational potentials, to advanced texts on tensor multipoles, radiation patterns, scattering theory and numerical methods such as the fast multipole method. Books typically emphasize both analytical derivations and practical applications across electromagnetism, classical gravity, acoustics, quantum mechanics and molecular modelling, and may include computational algorithms, convergence and error analysis. Intended audiences span advanced undergraduates and graduate students learning the formalism to researchers needing specialized techniques for analytical simplification or large-scale simulation.

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