Yes, you can apply for Permanent Residency (PR) in Italy after completing 5 years of legal stay and work. After finishing your Master's degree, you can stay for up to 12 months on a job-search permit. Once you find a job and get a work permit, your stay starts counting towards PR. Highly skilled workers with an EU Blue Card can apply for PR in just 3 years. Italy's PR allows you to live and work in Italy without any restrictions.