During 1997-2000 Dyngjujökull, one of the major outlet glaciers of the main Icelandic ice cap Vatnajökull, surged. This event was captured by ERS 1 and 2 satellites flying in tandem mode, enabling the use of InSAR to monitor the motion of the glacier. Since a major limitation of InSAR is its sensitivity to deformation in only one dimension, the research presented in this M.Sc. thesis searched the most accurate method of extracting azimuthal deformation using InSAR. Starting from a theoretical framework, the available methods are explored and corresponding measurement uncertainty formulas are derived. Currently available software enables the possibility to underpin the theoretical findings by performing different tests to compare two methods that are widely used in the InSAR community. Results show the presence of azimuthal shifts corresponding to TEC variations in the Earths ionosphere, which partly distort the along-track deformation. To solve this, the nature of this signal is studied and a filtering method is designed. Consequently, the corrected azimuth interferograms are used jointly with LOS interferometric data in a Markov Random Field minimum energy method, optimized by Simulated Annealing to derive 3D flow fields of the Dyngjujökull glacier in surge. This glaciology method is tested for its response behavior using synthetic data. The testing schemes involved mainly noise propagation and assessing the influence of different weighting factors in the optimization of the 3D flow outcomes. Knowing the limitations of the glaciology method, 3D flow fields are derived with real input data accordingly. The results show both horizontal- and vertical velocities corresponding to observational data. Finally, the presence of a process similar to a system of linked cavities as the subglacial hydrologic mechanism of surging glaciers is indicated by the glaciological outcomes.