Having rewatched it last weekend, I think this Marco Tullio Giordana's movie could be a good suggestion for learners of Italian that ask for Italian series. At least it gets close to them because, in spite of being released as a movie, originally it was thought as a miniseries of four episodes (the total length is more or less six hours), and so it was broadcasted on TV. The movie is about the story of a fictional family, and in particular of two brothers, spanned from the '60s until recent years, walking through all the key events of modern Italian history. It was released in a period in which similar titles were produced, that shares actors and that could be of some interest too: one is the director's former work, "I cento passi" (this one in my opinion is even better), and the other is "Buongiorno notte" by Marco Bellocchio.

A little grammar note, since we are on a language site: "La meglio gioventù" is named so after a book of poems by Pier Paolo Pasolini, and it is actually a poetic licence / a regionalism (the correct form is "La migliore gioventù").

Hope you enjoy it! If you watch it, feel free to comment here.