This thesis will examine the velocity structure of Austfonna, a large ice cap in the Svalbard archipelago. The remoteness of its location had previously hindered detailed observation by traditional methods, but indirect evidence suggested that it had the potential to be dynamically interesting. A recently developed remote sensing technique, SAR interferometry (inSAR), has allowed us to obtain the most detailed map of Austfonna's topography to date, plus unprecedented synoptic measurements of its velocity field. A four year time series of data acquired by the European Remote Sensing satellites ERS-1 and ERS-2 has been used to delineate active and inactive areas of the ice cap, which suggest that past ideas about Austfonna's thermal structure may need to be re-examined. It has also revealed large temporal velocity variations in one of its major drainage basins. These are difficult to classify because intermittent sampling has prevented us from determining their temporal wavelength, and also because globally the database of observed glacier velocity variations is so sparse that the range of possible variable flow scenarios is unknown. The work here demonstrates the huge potential for inSAR in helping to resolve such issues, and in providing an invaluable resource for scientists monitoring the stability of the world's ice fields.