The visa · Part A: What the visa is, and how it works
What can I do in other Schengen countries, and what can I not?
Short answer: Holding a valid Italian type D visa or residence permit, you may travel in the other Schengen states for up to 90 days in any 180 day period (German Federal Foreign Office). That is a Schengen wide rule, not an Italian concession.
What it allows
Short visits. A weekend in Vienna, a conference in Barcelona, a holiday in Greece, seeing relatives in France. Carry your passport and your Italian visa or permit card every time. A permit card on its own is not a travel document.
What it does not allow
- Living in another country. The 90 in 180 allowance is for visits. Your residence is Italy.
- Working in another country. Your permission to work comes from your Italian permit and applies in Italy.
- Studying a full program somewhere else. Your pre enrolment and permit are tied to the Italian course you named.
One thing I do not know
How border officers treat a student travelling while their permit is still only a receipt and the visa has expired. Reports differ, I found no published Italian guidance, and I am not going to guess on something that can strand you. If your visa is expiring and your card has not arrived, ask the Questura or a patronato before you book anything.
This page explains official rules in plain language. I am not an immigration adviser and I do not give visa advice. For that, always use official government sources. Rules change: confirm with your university, the embassy and VFS before you act.