The initiation and maintenance of (reentrant) arrhythmias is facilitated by local heterogeneities in cardiac activation and repolarization. Detection of these heterogeneities by cardiac mapping is important for guiding local therapy and for early risk stratification of patients, and is presently mostly performed by invasive techniques. A non-invasive method for localization of functional heterogeneities may help the treatment of patients with life threatening ventricular arrhythmias, may support risk stratification and may help to reduce mortality caused by these arrhythmias. This thesis investigates a non-invasive method to determine and localize functional repolarization heterogeneities based on potentials measured at the body surface. It demonstrates that parameters that highlight multiple repolarization moments in the standard 12-lead ECG, better characterize the underlying repolarization gradient than the single time point of latest global repolarization (QTtime). For further localization of possible heterogeneities, this thesis uses the equivalent dipole layer (EDL) method for the solution of the inverse problem of electrocardiography; the mathematical reconstruction of cardiac electrical activity from body surface electrograms and a geometric model of the torso. The accuracy was investigated in in-silico, ex-vivo, and in-vivo settings, showing good correlations with gold standard repolarization times, even in the presence of noise, abnormal repolarization or myocardial infarction. In addition, comparison of the EDL method with the more commonly used epicardial potential (EP) method shows that both methods provide accurate reconstruction of cardiac activation and repolarization patterns and beat origins, with the EDL method showing a better correlation for activation timings and beat origins than the EP method. Although the use of this technique for noninvasive mapping of repolarization is promising, we provide directions for future research to improve accuracy of inverse reconstruction