Electrons represent elementary magnets because of their spin magnetic moment, leading to paramagnetism, and their orbital magnetic moment, causing diamagnetism. In an external magnetic field the magnetization of a paramagnet is described classically by the Langevin function, to be replaced by the Brillouin function in the case of quantization effects. In a ferromagnet the elementary magnets are spontaneously oriented along a distinct direction. The first quantum mechanical explanation was proposed by Heisenberg, based on the exchange interaction between the electrons of two atoms. The perfect order of the elementary magnets can be perturbed due to the thermal excitation of spin waves, which also contribute to the specific heat and affect the electronic transport properties. In addition to ferromagnetic order, other forms of the spin magnetic order are possible, such as antiferromagnetism. The recent advances in the fabrication of well-controlled multilayer structures lead to important technical applications of giant magneto-resistance and to the birth of the new field of spintronics.