Magnetic resonance imaging (MRI) magnetic susceptibility mapping (SM) enables the calculation of the magnetic susceptibility of biological tissues based on the signal phase of a gradient-recalled echo (GRE) MRI acquisition. Because deoxygenated haemoglobin is paramagnetic, SM can be used to calculate the χ of venous blood which is proportional to venous oxygen saturation (SvO2). In this thesis, I investigated the feasibility of SM for the study of brain arteriovenous malformations (AVMs). AVMs are congenital vascular anomalies characterised by arteriovenous shunting through a network of coiled and tortuous vessels. Because of this anatomy, the venous drainage of an AVM contains high-pressure mixed arterial and venous blood. I investigated whether SM could detect any resulting increased oxygenation in the draining veins. Using numerical simulations and healthy volunteer data, I focussed on optimising the acquisition and processing of GRE phase data to achieve the best possible accuracy and precision for venous SM. I showed that acquiring multi-echo versus single-echo GRE data led to more accurate and precise susceptibility, and that combining the signal from multiple echoes before applying Laplacian-based phase unwrapping or background field removal increased the susceptibility’s accuracy. Based on healthy volunteer and patient data (before and after gamma knife radiosurgery (GKR)) I investigated the feasibility of SM of brain AVMs and the information provided by venous susceptibility on AVM pathophysiology. I showed that an AVM was detectable on a susceptibility map and that the AVM draining pattern had a significantly higher SvO2 compared to healthy veins. Flowing spins in blood cause an additional susceptibility-independent component in the GRE signal phase. Because clinical multi-echo GRE protocols, including the one developed here to study brain AVMs, do not compensate for flow-induced dephasing, I investigated the effect of flow compensation on venous susceptibility and SvO2 measurements and found only a minimal effect