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We give a review of Boson expansion methods applied in the quantum theory as e.g. expansions of spin, bifermion and Fermion operators in cases of the finite and infinite number of degrees of freedom. The basic purpose of the paper is to formulate the most general criterions allowing to get so called finite spin approximation of any given Bose field theory, and the class of Fermion theories associated with it. Quite the converse, we need also to be able to reconstruct the primary Bose field theory while any finite spin or Fermi systems are given.