Italy in the High Middle Ages
By about 900 AD, the Holy Roman Emperors began to lose power over Northern Italy, and Northern Italy divided into a lot of independent city-states. This arrangement was a lot like in classical Greece, or in West Asia in the Sumerian period. Some of the more important cities were Genoa, Florence, and Pisa. Each city was independent, and they frequently had wars with each other and with the Papal States to their south, as well as with the French to the north. Sometimes the Holy Roman Emperor tried to get control of these North Italian cities again, but he never really managed it.
Around the year 1000 AD, a new city called Venice, in Northern Italy near Greece, became very rich. Venice was supposedly under the rule of the Byzantine Empire, but really Venice was strong enough that the Byzantine Emperors couldn't tell Venice what to do.
In the center, the Papal States were also pretty weak between 900 AD and about 1200 AD. Still they held onto the whole middle of the Italian peninsula. Mostly the Popes were able to do this because they had the help of the French kings. The French kings were afraid that the Germans (the Holy Roman Emperors) would take over Italy and become more powerful than France. So the French kings always helped the Popes when the Germans attacked them.
More about High Medieval Italy
Early Medieval Italy
Late medieval Italy