We report the development, experimental verification, and application of a general theory called [Fe]MRI (pronounced fem-ree) for the non-invasive, quantitative molecular magnetic resonance imaging (MRI) of added magnetic nanoparticles or other magnetic contrast agents in biological tissues and other sites. [Fe]MRI can easily be implemented on any MRI instrument, requiring only measurements of the background nuclear magnetic relaxation times (T1, T2) of the tissue of interest, injection of the magnetic particles, and the subsequent acquisition of a pair of T1-weighted and T2-weighted images. These images, converted into contrast images, are subtracted to yield a contrast difference image proportional to the absolute nanoparticle, iron concentration, ([Fe]) image. [Fe]MRI was validated with the samples of superparamagnetic iron oxide nanoparticles (SPIONs) both in agarose gels and bound to human prostate tumor cells. The [Fe]MRI measurement of the binding of anti-prostate specific membrane antigen (PSMA) conjugated SPIONs to PSMA-positive LNCaP and PSMA-negative DU145 cells in vitro allowed a facile discrimination among prostate tumor cell types based on their PSMA expression level. The low [Fe] detection limit of ~2 μM for SPIONs allows sensitive MRI of added iron at concentrations considerably below the US Food and Drug Administration's human iron dosage guidelines (<90 μM, 5 mg/kg).