Ian G. Macdonald (11 October 1928 – 8 August 2023) was a British mathematician who made important contributions to algebra, geometry, Lie theory, combinatorics and special functions. He is renowned for the introduction of the Macdonald polynomials and his foundational work on symmetric functions.Anne-Marie Aubert is a French mathematician, director of Research at CNRS and leader of the team "Automorphic Forms" at the Institut de Mathématiques de Jussieu - Paris Rive Gauche. She is known for her contributions to the representation theory of p-adic groups, character sheaves, Hecke algebras and the Langlands program, in connection with noncommutative geometry.

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• Introduction. I Basic properties of spherical functions.- II Groups of p-adic type.- III Spherical functions on a group of p-adic type.- IV Calculation of the spherical functions.- V Plancherel measure.