Regioni, Province, Comuni
Italy is a Republic made of 5 constitutive elements: Regioni, Comuni, Stato, Province and Città Metropolitane.
The Stato Italiano (Italian Nation/Country) is divided into 20 Regioni, basically 20 big districts (see pic below): Valle d'Aosta, Lombardia, Piemonte, Liguria, Veneto, Trentino-Alto-Adige, Friuli-Venezia-Giulia, Emilia-Romagna, Toscana, Marche, Umbria, Lazio, Abruzzo, Campania, Molise, Puglia, Basilicata, Calabria, and the two big islands Sicilia and Sardegna.
Each of these Regioni has a Capoluogo di Regione (Chief place of the region/district), which generally is the most important city of that district (the most populated as well) in which there are the all the offices that control the whole area and connect it directly with the Stato's ones.
Here the Capoluoghi di Regione for each region:
Valle d'Aosta (Aosta), Lombardia (Milano), Piemonte (Torino), Liguria (Genova), Veneto (Venezia), Trentino-Alto-Adige (Trento), Friuli-Venezia-Giulia (Trieste), Emilia-Romagna (Bologna), Toscana (Firenze), Marche (Ancona), Umbria (Perugia), Lazio (Roma), Abruzzo (L'Aquila), Campania (Napoli), Molise (Campobasso), Puglia (Bari), Basilicata (Potenza), Calabria (Catanzaro), Sicilia (Palermo) and Sardegna (Cagliari).
There are 5 Regioni a Statuto Speciale (meaning that they can control themselves also in order to provide to the minorities on their soil. They basically can keep a bigger amount of taxes and can use it for school, health and other needs, while the other Regioni have to ask the State). These Regioni are Sicilia, Sardegna, Friuli-Venezia-Giulia, Trentino-Alto-Adige (also to protect the German speaking minority; btw it has the two Province autonome Trento and Bolzano as well, meaning those two are quite indipendent from the Region too), and Valle d'Aosta (also to protect the francophone minority - there's also a german minority as well here btw, on the part halfway with Piedmont: the Walsers).
Inside of each Regione, there are smaller areas/district called Province. Each Provincia has a Capoluogo di Provincia, which is basically, as the Capoluogo di Regione, the most important city of that small area (all this is made to control more easily and accurately each area). Check this:
The number of the Capoluoghi di Provincia, as you can see, can vary according on how big each Regione is.
In Piedmont, for example, we have 8: Torino (which has, as the other Capoluoghi di Regione, a "double job" let's say), Asti, Alessandria, Biella, Cuneo, Novara, Verbano-Cusio-Ossola (Verbania: the noun VCO is bc it's the whole area's name, the capoluogo is Verbania, which is made of two smaller city on the Lake Maggiore... yeah not easy to grasp but it's basically an exception and you don't have to remember it) and Vercelli.
Inside of each Provincia there are the Comuni: Comuni are even smaller areas, and are basically... infinite? I mean, there could be a hundred even in the smallest Provincia. Take this last pic and imagine to divide it all into even smaller parts. Some Comuni are so small, they're made of a few inhabitants, but if a place it's too far from another, it is better controlled by making a different Comune out of it (connecting the two could let you have a bigger amount of people together but that's not what we aim to do). We rather keep it small, let's say. Also to not mess up with the different identities on the territory (there could also be a different "dialect" spoken between two very close villages/Comuni).
Città Metropolitane: are some of the Capoluoghi di Provincia (but also di Regione) that have very important powers. They are all kinda big cities that are basically made of more different Comuni (districts) and work on them all as if they were one single thing.
The Città Metropolitane are Roma Capitale (Roma has often the noun "Capitale" in its name because it's Italy's capital city), Torino, Milano, Venezia, Genova, Bologna, Firenze, Bari, Napoli and Reggio Calabria, with the recent adds of Cagliari, Sassari, Palermo, Catania and Messina. (read here for more)
