<p>Quantitative susceptibility mapping (QSM) is a promising technique to study tissue properties and function <em>in vivo</em>. The presence of a susceptibility source will lead to a non-local field variation which manifests as a non-local behavior in magnetic resonance phase images. QSM is an ill-posed inverse problem that maps the phase back to the susceptibility source. In practice, the phase images are usually contaminated by background field inhomogeneities. In this thesis, several technical advances in QSM have been made which accelerate the data processing and improve the accuracy of this ill-posed problem. For background field removal, the local spherical mean value filtering (LSMV) is proposed, in which the global phase unwrapping is bypassed. This algorithm improves the time-efficiency and robustness of background field removal. For solving the inverse problem, an improved version of the k-space/image domain iterative algorithm is demonstrated using multi-level thresholding to account for the variation in the susceptibilities of different structures in the brain. The susceptibility maps could be used to generate orientation independent weighting masks, to form a new type of susceptibility weighted image (SWI), referred to here as true-SWI (tSWI). The tSWI data show improved contrast-to-noise ratio (CNR) of the veins and reduced blooming artefacts of the microbleeds. Finally, it is shown that the effective magnetic moment, being the product of the apparent volume and the measured susceptibility of the small object, is constant. This can be used to improve the susceptibility quantification, if <em>a priori</em> information of the volume is available.</p> / Doctor of Philosophy (PhD)