Magnetic resonance imaging (MRI) has made important contributions to the understanding of the dynamics of the disease process of multiple sclerosis (MS) in vivo and has an established role in the diagnosis of MS. Despite this, conventional MRI is only partially helpful in understanding the disease and predicting ultimate clinical outcomes. The lack of imaging biomarkers in MS also limits the development of therapeutic interventions that can eventually help treat the various symptoms of MS, including the common finding of cognitive impairment. In this dissertation, multi-modal MR imaging acquisition and analysis techniques were applied with the goal of attaining more sensitive methods for the quantitative characterization of the MS disease processes, especially those that might reflect the underlying pathological mechanisms related to cognitive decline in relapsing-remitting multiple sclerosis. Using advanced volumetric analysis techniques, significant gray matter (GM) atrophy in both cortical and subcortical regions was found in MS brains, where selective patterns of GM atrophy correlated with cognitive decline. Through diffusion tensor imaging (DTI), white matter (WM) integrity was examined, and the advanced DTI analysis methods employed allowed for the identification of widespread WM alterations in MS. With magnetic resonance spectroscopy (MRS), evidence of metabolic abnormalities was demonstrated in normal-appearing WM and GM in MS. Overall, this body of work advances our knowledge in relating MR metrics to underlying disease processes, and improving image-based characterization of cognitive decline over what is seen with conventional imaging. The results of this work may contribute towards developing future clinical metrics that comprehensively evaluate disease accumulation in patients, facilitating therapy development and monitoring, and thus improving quality of life for people with MS.