First, many-boson states are discussed and boson creation- and annihilation operators are introduced. The Hamilton operator of the interacting boson model is expressed in terms of Casimir operators. The first special case of this model including electromagnetic transitions is discussed and compared with experimental data. An elementary introduction to Lie algebras is followed by an analysis of the group theoretical aspects of this model. Neutrons and protons are treated separately in the proton-neutron interacting boson model, which is compared with many experimental data. Even-odd nuclei can be investigated with the interacting boson-fermion model. This report is directed towards nuclear physicists and students who are familiar with the elements of quantum mechanics, classical electrodynamics and nuclear physics. Great store has been set by a consistent and didactically constructed presentation. Many subjects are discussed which until now could only be found in the research literature.

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