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Various works performed by the present authors in the 1990s are reviewed. Thetopics discussed in this paper are mainly related to the time-evolution of thecoherent and the squeezed states of the systems obeying the su(2)- and thesu(1,1)-algebra. The formulations are based on the basic idea of the bosonmapping and the TDHF theory in canonical form. Under the time-dependentvariational procedure for trial states appropriately chosen, the time-evolutionof the systems under investigation is described. Further, it is shown that thismethod enables us to obtain the classical counterparts of the original quantalsystems.Comment: 65 pages using PTPTeX.sty. To appear in Progress of Theoretical  Physics Supplement ``Selected Topics in Boson Mapping and Time-Dependent  Hartree-Fock Methods.

Time-Evolution of the Coherent and the Squeezed States of Many-Body Systems Based on the Basic Idea of the Boson Mapping and the TDHF Method