Added 15 December 2015:
Volume Two, The Story of a New Name, takes the story of Lina and Lenù into their early twenties. Lina has a child and leaves her husband for a life of hard work and poverty; Lenù leaves Naples for Pisa, graduates from university and aged 23 publishes a novel. Once again, I felt that Lina and Lenù are two sides of one person. Lina's notebooks - entrusted to Lenù - provide a simple literary device which enables Lenù to know everything about her absent friend's life.
The chapterettes (125 in 471 pages) remain highly charged and constantly provide fresh material. At times, I visualised it as a TV soap opera or sitcom (without the com) - a fixed cast of characters leading dramatic lives. It lends itself to TV forms more than to treatment as a film - a film would have to edit out three quarters of the material
The volume ends dramatically, like its predecessor, creating the space for the third volume:
Added 3 January 2016: The two final volumes follow the lives of both women into their sixties and now much more space is given to Lenù's narrative of her own life, which is both unsparing and defensive.
In volume three, I was puzzled by the disappearance of the Camorra and its replacement by an assortment of "fascists" and "criminals". To be honest, I wondered if the author had been spoken to and told to be more careful. Volume Four brings the Camorra back but in a way which rather confirms that feeling - Lenù's sister marries one of the two principal Camorrists of the first volume.
There is a lot here about Italian politics in the 1980s and the ways in which Italy was (and still is) a failed state which has never been able (for example) to offer a fit for purpose Justice system to its citizens and so has provided the space in which the Mafias continue to thrive. If the State won't offer you protection, then the Mob will: Lina is explicit about this at one point. As recently as 2011 The World Bank rated Italy 158 out of 183 countries "for the efficiency of its justice system in enforcing contracts", just three places above Afghanistan. [ See my review of John Dickie's Mafia Republic on this website, 21 July 2013]
There is lots, lots more and in the end perhaps too much: the narrative structure is really "and then and then and then ..." which doesn't create pace and which does not create emotional climax for the reader at crucial moments (as when Lina's young daughter disappears). The absence of authorial humour from any of the hundreds of scenes is striking.
The editing of these books is impeccable. I could find fault with only two things: the occasional use of pseudo-generic "he" by the translator and a reference at page 105 in volume 4 to "Thailand" where the context of 1980s political debate clearly indicates that it should read "Cambodia" at the time that it was the Kampuchea of the Khmer Rouge.