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: The study which fonns the second volume of this series deals with the interplay of groups and composite particle theory in nuclei. Three main branches of ideas are deÂ veloped and linked with composite particle theory: the pennutational structure of the nuclear fermion system, the classification scheme based on the orbital partition and the associated supennuitiplets, and the representation in state space of geometric transÂ fonnations in classical phase space. One of the authors (p. K.) had the opportunity to present some of the ideas underÂ lying this work at the 15th Solvay Conference on Symmetry Properties of Nuclei in 1970. Since this time, the authors continued their joint effort to decipher the conceptual strucÂ ture of composite particle theory in tenns of groups and their representations. The pattern of connections is fully developed in the present study. The applications are carried to the points where the impact of group theory may be recognized. The range of applications in our opinion goes far beyond these points.