Magnetic resonance imaging (MRI) offers a good tissue contrast and the ability to visualize many disease related morphologies. The work presented in this thesis investigates the study of underlying structure of the brain using quantitative methods with a special emphasis on quantitative susceptibility mapping (QSM). Magnetic susceptibility reflects the interaction of a material to the magnetic field and measures in biological tissues the magnetic susceptibility of inclusions. The reconstruction of QSM requires further processing steps as the magnetic field produced by the sources needs to be disentangled from the orders of magnitude bigger background field. The produced field also depends not only on the shape and the orientation, but also on the anisotropy of susceptibility and the microstructural compartmentalization of the biological source. For this reason, reconstruction methods need to be capable to calculate accurate values for different brain regions as well as applicable in the everyday clinical diagnosis. Within the framework of the thesis a data acquisition protocol based on a multiple-echo gradient echo sequence as well as a post-processing protocol was implemented. One of the processing steps, the background removal method, was applied to preserve the brain regions close to the cerebrospinal fluid (CSF). This method outperforms state of the art methods in this regions but is computationally intensive. Different brain regions were studied using quantitative methods with special emphasis on the QSM. A new method, modulated closed form solution, with extremely fast computational time is proposed. The comparison with other single orientation methods revealed similar results and the highest correlation to the state-of-the-art method (COSMOS) in the deep gray matter. The R2* maps calculated from the same dataset are also able to distinguish the deep gray matter structures with a similar quality. However, QSM shows a higher sensitivity in early stage multiple sclerosis lesions as well as white matter-gray matter structures. In the human cortex the obtained cortical maps show enhancement of primary sensory cortex, which is known to be highly myelinated, on three evaluated quantitative contrasts R1,R2* and susceptibility. The contrasts based on the relaxation rates, R1 and R2*, show a monotonically decrease from the white matter to the CSF imitating the decrease in iron and myelin. The susceptibility behaviour is more complex as iron and myelin content introduce an opposing sensitivity, allowing to study iron and myelin content when combining the three contrasts. The microstructural organization of white matter influences the R2*, R2 as well as field map from which QSM is calculated. This structure leads to an orientation dependence of the studied contrasts and for QSM the spherical assumption is not valid anymore. Therefore a new QSM method is introduced, which includes the Lorentzian correction in white matter. Main fibres such as forceps major and minor were analysed for the three different quantitative contrasts. The anisotropic component associated with susceptibility is similar for the relaxation rates whereas the isotropic component of R2* shows a higher variability. The resulting deep gray matter structure of the new QSM method remained similar to the state-of-the-art method when comparing the isotropic component but calculates physically meaningful susceptibility maps with improved contrast between known fibre bundles.