Here indeed is a difficult book to review: it is so obviously a work of impressive scholarship, yet it has a number of notable shortcomings.
The comment has been made in other reviews that Green is an elegant writer, but I believe that only superficial readers or the author's friends and associates would say that. Green's writing has important and obvious flaws that prevent the book from being what it might have been.
While he sometimes offers elegant sentences, he too often offers convoluted sentences or sentences stuffed like long, fat sausages, sometimes even diverging from the subject in the course of setting down his words. He also maintains a rather superior gesturing in his prose. I know the effect Green likely hoped he was achieving - the majesty of Edward Gibbon or Thomas Macaulay - but he just does not succeed.
He is often an extremely pedantic writer, generously sprinkling his text with words and phrases not just from Greek and Latin but German and French, and always selecting obscure words or Latinisms where solid Anglo-Saxon words would serve better.
There are indeed times when a foreign expression captures the special sense of a concept that a translation may loose, and I have no objection to their use where that is true, but that is not the case here.
I very much object to the gratuitous use of foreign words and phrases to display an author's learning, something which makes the work less accessible to many while simply annoying others with a gimmick related to the use of "as the eminent, such-and-such prize-winner once said..." to bolster a quoted source's authority (something Green spares us). The effects are poisonous in a work of this nature.
Yet Green knows a great deal about his subject, and I certainly learned from him despite the faults. His interpretation of the Hellenistic world after Alexander as representing a decay and gradual departure from (reaching almost a bastardization of) Greece's true classical period is interesting, and he mounts some strong supporting evidence for the view.
The book is not properly understood as a history, because large portions of it are arguments of positions on historical or philosophical or esthetic or moral issues. There's nothing wrong with that, but potential readers should be aware of the fact.
There is such a huge cast of characters involved in the three great divisions of Alexander's conquests over a couple of centuries that one loses track of some of them in the narrative, many of course being minor or simply having left few records, but one might have hoped for a clearer, more sustained narrative of the truly important figures. There is a sense of fragmentation here which may be just the fault of a fragmentary record.
There is a considerable difference in Green's success in explaining some events. He sometimes leaves you mentally saying, "Yes, indeed," while other times he leaves you saying, "What?"
Despite the flaws, this is a significant book and one worth reading by anyone interested in the Hellenistic era and in the successors to the dead Alexander and in the rise of imperial Rome.