This is a research-oriented course integrated with mathematical modeling and analysis and scientific computation and visualization. We first introduce basics of bioelectromagnetism and MRI in the context of MREIT, MREPT and QSM. We deal with each modality where we explain associated measurement methods, interrelations between obtained MR data and image contrasts, image reconstruction algorithms, experimental techniques and potential biomedical applications. We also discuss mathematical theories including error estimates, uniqueness and some challenging open problems.