The relationship between magnetic properties of rare-earth metals and the electron structure of the f shell is considered. Simple concepts are used to show how many-electron quantum numbers of the spin, orbital and total angular momenta of the f shell are related to the Curie temperature, magnetic moment, magnetic anisotropy, and other properties of a rare-earth metal and how modern mathematical apparatus for the addition of angular momenta and specifically the Racah algebra can be used to calculate these characteristics. The differences in respect of the nature of magnetism between rare earths and metals in the iron group with partly filled d shells are discussed. A clear interpretation is given of the periodic dependence (with a period of 1/4) on the number of the f electrons exhibited by magnetic properties (particularly in the case of the magnetic anisotropy) within the rare-earth series. A brief discussion is given of magnetic properties of alloys in relationship to the local anisotropy.