Permit of stay
From Students@SISSA wiki
If you are a non-European/EEA citizen and you wish to study your Ph.D. at SISSA, you must apply for a permit of stay in order to legally stay in Italy. With the visa issued by the Italian Consulate/Embassy in your country of origin, you must apply within 8 working days for your permit of stay.
You should always carry with you your permit to stay or the post-office receipt issued when handling the application.
STEP 1: APPLICATION FOR THE PERMIT OF STAY
STEP 2: APPOINTMENT AT THE QUESTURA
STEP 3: GETTING YOUR PERMIT OF STAY
TIPS
To the appointment take all the documents you have. :)