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The Hartree-Fock-Bogoljubov equations in the rotating frame (Cranking model) are used to describe the behaviour of rapidly rotating nuclei. The rotation is expected to predominantly change the single particle motion, the pair correlations an the nuclear shape. The quasi particle motion in a rotating potential is extensively discussed. The symmetry quantum numbers parity and signature are used for the classification of the levels. The angular frequency plays a key role. Its experimental determination is discussed. The experimental excitation energy and angular momentum of the quasi particles are defined. The experimental spectra may be understood in terms of configurations of independent quasi particles. The disappearance of pair correlations due to rotation is analysed. The fluctuations of the pair field stabilize the correlations. The transition to the unpaired state consists of few jumps due to the break up of individual nucleon pairs. The calculated nuclear shape remains approximately unchanged in a large interval of angular momentum. At high momenta it jumps to larger deformation. This reflects how the shell structure influences the deformation energy. (Atomindex citation 12:601406)