The detection of high-energy extraterrestrial neutrinos is one of the ultimate challenges in astroparticle physics. Besides opening a new observational window, neutrino astronomy has the potential to solve the long-standing question of the origin of cosmic rays and can also determine the production mechanism of high energy photons. The IceCube observatory currently under construction at the South Pole is the most advanced project providing a realistic chance to detect the first neutrino sources. While the construction is expected to be completed during the period of this project, physics operation with the intermediate detector has already started during May 2007. A significant contribution to the construction and early maintenance of the IceCube detector will be given with the proposed fellowship. The continously taken data from the gradually growing detector will accumulate already in 2009 to the equivalent of one year of full IceCube operation, giving rise for the hope of first discoveries during the project period. Within this project novel and more advanced data analysis methods will be developed and applied on the largest sample of high energy neutrinos ever available. The most recent astrophysical knowledge will be included in the optimization of the searches as well as all the neutrino detection channels (muon track and cascade). The focus will be on the search for neutrinos from gamma-ray bursts (GRBs) as prime candidates for extragalactic cosmic ray sources.