This is quite an easy read for non-military people and ought to be on the reading list of politicians in particular. It undoubtedly does what it says on the tin by spelling out the developing nature of war into the 21st century.
It is probably not worth getting hung up on the definitions of the phases - they are just a useful structure. Nevertheless, the book provides a good summary of how fourth generation warfare (as defined) started with Mao before World War 2 and focuses on the direct destruction of the enemy's political will. It charts progress and refinements from Mao through Vietnam, the Sandanistas, the Palestinian Intifada and into Al-Qaeda, Iraq and Afghanistan and shows how insurgents form loose networks that are resilient and difficult to destroy.
It is made clear that 5GW has already started but worrying about that is to miss the point that modern "opponents" seek to win by wearing down political will through a long drawn-out struggle. They don't have to "win" - only stay in the struggle until the other (democratic) side gives-up and goes home. There are lessons here for policy makers and the military.
No book can cover all aspects but this is a useful contribution to the debate to be taken with other inputs. There is an extensive reference section, but no mention of Gunnar Heinsohn and his demographic theory of war (Sons of World Power etc., in German but still not in English) despite a clear lead into the subject on page 183 about "angry young men with time on their hands". A pity - it would be interesting to compare demographic profiles for the listed countries/campaigns and to suggest alternative policy responses as a result. Perhaps someone else can oblige?