Stroke is one of the leading causes of death and disability worldwide with 20% of ischemic strokes attributed to carotid atherosclerosis. In recent years, morphological characteristics of atherosclerotic plaque such as a thin fibrous cap, large lipid-rich necrotic core, intraplaque haemorrhage and ulceration have shown correlations with subsequent clinical events. High resolution, multi-contrast magnetic resonance imaging (MRI) can qualitatively identify these features and monitor disease progression. Compared to traditional contrast weighted imaging, quantitative MRI could provide an objective assessment of disease. Therefore, the general hypothesis investigated in this thesis is: Quantitative MRI methods can be used to acquire objective biomarkers of carotid vessel wall and atherosclerotic plaque, with high accuracy and good repeatability. The research presented in this thesis describes the use of multiple quantitative MRI methods to evaluate the carotid vessel wall. These include dynamic contrast-enhanced (DCE) MRI analysis for the assessment of plaque inflammation/neovascularization and the development of black-blood quantitative T2/T2* mapping sequences for plaque component characterisation. The acceleration of the sequences was also investigated using a combination of compressed sensing (CS) and parallel imaging (PI). Chapter 3 investigated the hypothesis that plaque functional characteristics and surface morphology can be evaluated using a high temporal and spatial resolution 4D contrast-enhanced MRI/MR angiography (MRA) sequence. Chapter 4 tested the hypothesis that magnetisation prepared 3D fast-spin-echo (FSE) is the best sequence for in vivo T2 mapping. Four different black-blood T2 mapping sequences were developed and compared in phantom and volunteers. Chapter 5 tested the hypothesis that the optimised iMSDE 3D FSE T2 mapping sequence can be combined with CS and PI to further reduce the acquisition time without significantly affecting image quality and the measured T2 relaxation times. Chapter 6 investigated the hypothesis that compressed sensing can be used to reduce the overall examination time of a comprehensive multi-contrast MRI protocol, comprising black-blood T1 weighted, T2 weighted and proton density weighted sequences. Finally, Chapter 7 investigated the hypothesis that accurate 3D vessel wall R2* mapping can be achieved through black-blood preparation. In summary, this thesis investigated the use of multiple quantitative MRI methods in evaluating the carotid vessel wall and atherosclerotic plaque. The results demonstrate that quantitative MRI is an accurate and reproducible method for the carotid plaque characterization.