"The key principles of neoconservatisim as they developed from the mid-twentieth century to the present are deeply rooted in a variety of American traditions. Neoconservatism is a coherent set of ideas, arguments, and conclusions" (p13). So Francis Fukuyama dismisses those who challenge the existence of a unified neoconservative theme, or its underpinnings in American culture. These consistent themes are (pp 48-9):
1. "the nature of the regime matters to external behavior"
2. "American power has been and could be used for moral purposes" "the United States has special responsibility in the realm of security."
3. "The untoward consequences of ambitious efforts at social planning is a consistent theme in neoconservative thought"
4. Neoconservatives have "skepticism about the legitimacy and effectiveness of international law and institutions to achieve security and justice".
The largest chapter in the book on "Neoconservative legacy" then traces the history of the movement and how these ideas developed. Much of the rest of the book is a criticism of how these ideas were inappropriately applied in the Iraq war.
The book is not a refutation of neoconservatism. Quite the contrary, it is a sort of apology (in the traditional sense of the word), and a distinction between the ideology and how it was misunderstood or mistakenly applied.
I found the book very helpful in understanding the origins of the movement, and for an introduction to Leo Strauss, who according to Fukuyama is frequently misunderstood. Strauss appears to have influenced important intellectual figures such as Allan Bloom and Henry Jaffa, and "his students tended to see the United States as the apotheosis of the philosophical tradition from Plato and Aristotle, thus merging Strauss's philosophical concerns with American nationalism" (p23). This type of reasoning provides intellectual support for American exceptionalism.
As to the relationship of neoconservative ideas to those of other conservative traditions (social, religious and libertarian), according to Fukuyama from the 1970s onwards: "many neoconservative ideas were adopted by mainstream conservatives" and "many neoconservatives began adopting domestic policy positions of traditional conservatives (p38). This led to a convergence in views, despite the somewhat leftist origins of the movement.
How coherent is the doctrine? Fukuyama states that "neoconservatism's contemporary enemies vastly overstate the uniformity of views that has existed within the group" (p39), "those who argue that neoconservatism does not exist point to the fact that there is no established neoconservative doctrine," and because "neoconservatism is not monolithic does not imply it does not rest on a core of coherent ideas." So it exists, it is coherent, but it is not monolithic.
At the end, whether one accepts Fukuyama's argument, which is ultimately a justification of neoconservatism and a refutation of its purported application in the Iraq war depends most on one's acceptance of Fukuyama's four foundational principles. If one does accept these principles, then it is possible to construct a reasonable foreign policy which is consistent with the movements beliefs. On the other hand, not one of the four is uncontroversial.