The thesis at hand has successfully investigated and characterized the extended magnet system of the KATRIN experiment and implemented a detailed simulation model to take into account all field contributions. A concise modeling and understanding of the magnetic field close to the analyzing plane is crucial for a precise measurement and analysis of the neutrino mass with a sensitivity of 200 meV (90 % C.L.). A key aspect of the work performed here is that the contributions of individual magnets to the field in the analyzing plane in the spectrometer have been identified for various configurations. Based on these measurements, the previously undetermined remaining magnetic background field could be quantified. The advanced magnetic field model of this thesis allows to significantly reduce previously unexplained field deviations, verified by an in-depth analysis of extensive transmission function measurements with an electron gun, offering a sharp energy distribution and small angular spread. Of key importance thereby was a precise reconstruction of the emitted electrons of the electron gun in Monte Carlo simulations and the implement ... mehration of a realistic electron spectrum of the electron gun in the analysis framework. When all magnetic field contributions are taken into account, the transmission properties of the spectrometer can be determined with an accuracy level which is improved by a factor 3 in comparison to previous analyses. Correspondingly, the magnetic field there is determined to an unprecedented accuracy with a deviation between measurement and simulation of (3 ± 11) μT when a field of 363 μT is applied. Finally, the influence of identified magnetic field deviations on the neutrino mass sensitivity of the KATRIN experiment is studied by means of extensive ensemble tests. From this, an upper limit on the magnetic field of 585 μT in the KATRIN spectrometer is deduced to restrict the additional contribution to the systematic uncertainty budget to a level of 1 % for an optimal measurement of the neutrino mass.