Contents 1 . Introduction 2. Effect of ion multiplicity on electron exchange interactions i n crgstals 2.1 Generalized s-d(f) exchange interaction Hamiltonian allowing for exci-2.2 Generalized s-f exchange interaction Hamiltonian 2.3 Generalized direct exchange interaction Hamiltonian. Multiplicity waves 2.4 Generalized indirect exchange interaction Hamiltonian 2.5 Effect of ion multiplicity excitations on electric resistivity of metals 2.6 Effect of multiplicity excitations on the critical temperature of supercon-tations of spin multiplicity of d shells ductors 3. Spin s y s t e m multiplicity of the crgstal as a whole 3.1 Multiplicity indeterminancy of antiferromagnets 3.2 Multiplicity indeterminancy in the case of weak ferromagnetism 3.3 Multiplicity indeterminancy of helical magnetic structures References (Part I ) the establishment of the chemical valency of atoms [5], in t,he phenomenon of sensitized phosphorescence [6], in the photosynthesis of green plants 171, in the occurrence of stimulated radiation [8], in the resonance spin orientation in cosmic space [9], in the formation of Cooper pairs of superconductors [lo], and many others.Thus, multiplicity excitations are important not only for physical, but also for astrophysical, chemical, and biological phenomena.The quantum system of a gaseous or a condensed phase may deal both with mulbiplicity excitations of separate atomic particles, for example, magnetic ions, and the entire body (for example, of a crystal) as a whole. For instance, in the quantum theory of ferromagnetism the collective magnetic excitations, viz. x = 2 s + 1 , x = 2 J + l .