A monitoring system of the health condition and/or of physical activity for an individual, including a garment, dry electrodes made of graphene or conductive silicone, integrated with the garment and configurated for the detection of ECG signals related to the electric activity of the heart. Moreover, on the garment are also placed an electric energy accumulator and an elaboration and control unit for the elaboration of the ECG signals, and for their transmission to a remote reception system.