Nisbet's History of the Idea of Progress is really two books in one.
Book 1 (Chapters 1-7)
The first book is excellent. It casts a wide net to catch ancient and European figures writing about historical change from the ancient world all the way until 1900. Nisbet must have done years of research to be able to summarize and synthesize the views of dozens of ancient, medieval, and pre-modern writers on the topic of progress. For an overview of the development of the idea of progress in "Western" thought over this period, I cannot believe that anything more comprehensive exists.
Nisbet's overarching argument is that in the ancient world there were those who thought that history was cyclical -- sometimes even believing that history plays itself over and over again like a song on repeat -- and those who thought that history was progressive. Proponents of both historical narratives continued to exist throughout the middle ages. Sometimes the cyclical accounts were dominant (surprisingly Nisbet flags the Renaissance as such a period), and sometimes the progressive perspectives were at the fore, as in the Reformation in the 17th and early 18th century. Starting in the mid-18th century, however, progress became the dominant thread in understanding the world, tying together all sorts of political, economic, and sociological thought.
When one reads academic texts, sometimes one can smell the gunpowder from the battles outside. When Nisbet argues that ancient writers thought of history as progressive as much as they thought of it as cyclical, it seems he is arguing against other academics who think the ancients purely thought of history as cyclical. When Nisbet says that the Renaissance was a period in which people gave up on historical progress, he may be playing a contrarian to scholars who find the roots of the enlightenment belief in progress there. As a non-expert, the fact that there are presumably well-read people who hold other views makes me a smidgen less confident in Nisbet's conclusions.
Book 2: Chapters 8-Epilogue
The second book is Nisbet's opinions and predictions about the current state and future of both the idea of progress, and actual progress. This book is comically wrong about nearly everything. From Nisbet's view in 1980, it predicts among other things that people will stop learning about history, that the United States will lose its influence in the world (a few years after the book was published the Soviet Union fell), and the masses will lose interest in technological change and even life itself. More to the point, Nisbet predicts that people will stop believing in progress. My casual observation is that the opposite has happened. Many people believe that technology is driving history. My son asked me today if I think that I will live long enough to see flying cars. Techno-optimism and futurism are alive and well.
In the Epilogue, the clearly religious Nisbet argues that the only way to restore the belief in progress in Europe and the United States is through a Christian revival. He sees signs that this will happen. Nisbet thinks that European society was able to ride on the coattails of religion for awhile, but if Christianity does not take a stronger place in society, Nisbet predicts the end of both the belief in progress and the slow death of civilization itself.