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This work presents three new quantitative methods for magnetic resonance imaging. A method for simultaneous mapping of B1 and T1 (MTM) is developed and validated. Electric Properties Tomography (EPT), a method for quantitative imaging of dielectric properties of tissue, is presented. Based on EPT, separate (phase-based) conductivity and (amplitude-based) permittivity measurements are introduced. Finally, a B1-based method for patient-specific local SAR measurements is presented.