A monograph on the application of the method of separation of variables in partial differential equations and its relationship with group theory (the relationship between the Lie algebra of symmetry of the equation, coordinate systems in which the equation allows separation of variables, and the properties of the resulting special functions), belongs to the pen of an American mathematician. All solutions with divided variables of a number of classical equations of mathematical physics (Laplace, Helmholtz, Klein-Gordon, Schrödinger equations) were found, a large reference material on special functions is given.