This work explores and presents the principles of 'surface potential theory for the sphere,' in addition to those in the Euclidean space R3, and breaks new mathematical ground in dealing generically with potential theoretic aspects of gravitation and geomagnetism. The work covers a two-semester graduate course in the teaching cycle of geomathematics, but it can as well be used as a reference for researchers and aims at presenting the state of the art in three-dimensional Euclidean as well as two-dimensional spherical potential theory for applications in the geosciences-- Provided by publisher.