I've just got to the end of Season 3, loved every episode but now I need to go back to the start because the ending has triggered a memory from Season 1.
I read the first book, but strangely I have preferred watching the series. Usually I prefer a book to a dramatisation, but this production is just so perfectly presented- beautiful cinematography, you can see the Italian light and almost feel the sunshine, meticulous attention to details of the era, politics, fashion, cars, furniture, but most of all the excellent standard of acting.
If you are enjoying My Beautiful Friend, you might like The Lost Daughter, a film of another Elena Ferrante novel, starring Olivia Coleman, very similar themes. I think it's on Netflix.