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The high confinement mode (H-mode) is the operational scenario foreseen for ITER, DEMO and future fusion power plants. At high densities, which are favourable in order to maximize the fusion power, a back transition from the H-mode to the low confinement mode (L-mode) is observed. This H-mode density limit (HDL) occurs at densities on the order of, but below, the Greenwald density.\nIn this thesis, the HDL is revisited in the fully tungsten walled ASDEX Upgrade tokamak (AUG). In AUG discharges, four distinct operational phases were identified in the approach towards the HDL.\nFirst, there is a stable H-mode, where the plasma density increases at steady confinement, followed by a degrading H-mode, where the core electron density is fixed and the confinement, expressed as the energy confinement time, reduces. In the third phase, the breakdown of the H-mode and transition to the L-mode, the overall electron density is fixed and the confinement decreases further, leading, finally, to an L-mode, where the density increases again at a steady confinement at typical L-mode values until the disruptive Greenwald limit is reached.\nThese four phases are reproducible, quasi-stable plasma regimes and provide a framework in which the HDL can be further analysed.\nRadiation losses and several other mechanisms, that were proposed as explanations for the HDL, are ruled out for the current set of AUG experiments with tungsten walls.\nIn addition, a threshold of the radial electric field or of the power flux into the divertor appears to be responsible for the final transition back to L-mode, however, it does not determine the onset of the HDL.\nThe observation of the four phases is explained by the combination of two mechanisms: a fueling limit due to an outward shift of the ionization profile and an additional energy loss channel, which decreases the confinement.\nThe latter is most likely created by an increased radial convective transport at the edge of the plasma.\nIt is shown that the four phases occur due to a coupling of these two mechanisms.\nThese observations are in line with studies made at AUG with carbon walls, although in those discharges the energy loss was most likely caused by the full detachment of the divertor.\nThe density of the HDL depends only weakly on the plasma current, unlike the Greenwald limit, and can be increased by high heating power, again unlike the Greenwald limit.\nThe triangularity of the plasma has no influence on the density of the HDL, though improves the performance of the plasma, since the onset of the degrading H-mode phase occurs at higher densities.\nIt is explicitly shown that the HDL and also the L-mode density limit are determined by edge parameters. \nUsing pellet fueling, centrally elevated density profiles above the Greenwald limit can be achieved in stable H-modes at a moderate confinement. \nFuture tokamaks will have intrinsic density peaking. Consequently, they will most likely operate in H-modes above the Greenwald limit.