The trial will include 51 adult participants with Parkinson's disease and postural instability and gait disorders (PD-PIGD) and 20 age- and sex-matched healthy controls. At baseline (T0) patients will undergo neurological and cognitive/behavioural assessments, gait/balance evaluation, neuroimaging/neurophysiology assessments including brain magnetic resonance imaging (MRI), functional Near Infrared Spectroscopy (fNIRS) and Electroencephalography (EEG) acquisitions to assess brain activity, connectivity and structural changes, and blood sample. PD-PIGD patients will be randomly allocated in two training groups: the REHAB+SHAM group and the REHAB + STIM group. The REHAB+SHAM group will perform 2 cycles of dual-task gait/balance training consisting of action observation training (AOT) and motor imagery (MI) combined with practicing the observed-imagined exercises (an approach that has been demonstrated to be effective to improve gait and mobility in PD-PIGD), additionally they will undergo SHAM transcranial and trans-spinal stimulation. SHAM stimulation will be performed using the same montage used for transcranial and spinal stimulation (explained below), however an initial current is delivered and programmed to fade off in a brief period of time. The REHAB + STIM group will perform the same exercises combined with non-invasive stimulation. Non-invasive stimulation will be administered using tDCS with trans-spinal Direct Current Stimulation (tsDCS) or transcranial Direct Current Stimulation (tDCS) alone combined with SHAMtsDCS. This design will aid in determining not only whether non-invasive stimulation can enhance rehabilitation outcomes but also whether the combination of tDCS and tsDCS could lead to improved results compared to tDCS alone. The motor-cognitive training of the REHAB+SHAM group will consist of 2 cycles of SHAM stimulation and training lasting 6 weeks, 3 times per week, about 1 hour each session, separated by a 8-week washout period. The REHAB + STIM group will undergo 2 cycles of the 6-week training, separated by a 8-week washout period with a cross-over design: half of subjects will first receive 6-week training with tDCS+SHAMtsDCS followed by 6-week tDCS+ tsDCS, while the other half will follow the reverse order, according to a randomization procedure. After the training (i.e., 6-week visit \[W6\] and 20-week visit \[W20\]), PD-PIGD patients will be re-evaluated through neurological, cognitive/behavioural, gait/balance, neuroimaging/neurophysiology assessments and blood sample. These measures (except for MRI at 14-week \[W14\] visit) will be also repeated at W14 and 28-week follow-up visits to assess maintenance of results. 20 healthy controls will also be recruited and evaluated at baseline. They will undergo the same assessments administered to PD-PIGD patients at T0 (neurological, cognitive/behavioural assessments, gait/balance evaluation using gait analysis systems, neuroimaging/neurophysiology, blood sample).