Here are links to my chapter-by-chapter notes outlining this critical book. But please don't stick with the notes, pick up a copy of Cochrane's Christianity and Classical Culture for yourself--it is definitely worth both your money and time.
Preface: The goal of the book briefly stated.
Part I: Reconstruction
I. Pax Augusta: The Restored Republic: Explores the nature of the "eternal" state Augustus believed himself to have set up.
II. Romanitas: Empire and Commonwealth: Walks through the virtues and philosophical foundations for the Roman Empire, and their claims to be the final establishment of a political order.
III. Roma Aeterna: The Apotheosis of Power: Rome in this scheme becomes the real-world establishment of the sought-after transcendent Platonic ideal. All mankind may now live the happy and moral life.
IV. Regnum Caesaris Regnum Diaboli: This "Golden Age" quickly (immediately?) becomes a totalitarian dictatorship, embodying not the highest good but the worst aspects of human nature, only occasionally offset by glimpses of nobility.
Part II: Renovation
V. The New Republic: Constantine and the Triumph of the Cross: Constantine temporarily restored the old order, and tried to tap into the energy and spirit of Christianity as a new source of strength for the tottering Empire. This meant toleration for Christians, which further meant Christians had to re-think their political views.
VI. Quid Athenae Hierosolymis? The Impasse of Constantianism: Christians have to reevaluate how they and their beliefs relate to the pagan and secular foundations and goals of the Empire.
VII. Apostasy and Reaction: The pagan reaction against this intrusion of Christianity was passionate, but physically weak, and really just showed that paganism had run its course.
VIII. State and Church in the New Republic: Even as barbarians start to pour into the Empire, the Emperors attempt to uphold the old order by using Christian energy and enthusiasm as a source of power.
IX. Theodosius and the Religion of the State: Finally, Theodosius simply adopts Christianity as the official foundation of the Empire, and in doing so puts new wine into old wineskins and breaks the latter (the effect on the former is not Cochrane's concern here).
Part III: Regeneration
X. The Church and the Kingdom of God: But why didn't Christianity save Rome? Cochrane begins a contrast between Classical reason-based thought and the doctrines of Christianity, which include a view of personality and epistemology that are utterly incompatible with the Classical worldview.
XI. Nostra Philosophia: The Discovery of Personality: Augustine's view of man and personality as fundamentally affectionate and willing becomes the primary point of contrast between the two worldviews.
XII. Divine Necessity and Human History: History itself must be reexamined, and the sovereignty of God and the new view of human nature appropriately accounted for.