The Collapse of Complex Societies by Joseph Tainter is fantastic. It tries to establish a general theory behind past civilisational collapses. It looks at economic factors which lead societies into decline and argues that diminishing returns are a predictor and cause of collapse.

Collapse: How Societies Choose to Fail or Succeed by Jared Diamond is very good too. It focuses on case studies of societies which have collapsed for ecological reasons.

One book I'd recommend that hasn't been mentioned in the other answers is Toby Ord's The Precipice. It focuses on existential risk more broadly, rather than just on collapse, but several parts of the book are about civilizational collapse, or are quite useful for thinking about that topic.

I've also previously made "collection of sources that seem very relevant to the topic of civilizational collapse and/or recovery". You (or others) might find that collection helpful. It includes books as well as other types of sources. 

I definitely think this is a very important topic, and I'm glad to see EAs interested in it!

I have not explicitly searched out books to answer this question, but here is my understanding.

The best books have to be Asimov's Foundation trilogy.

The most relevant book to answer this question is Jared Diamond's Collapse: How Societies Choose to Fail or Succeed. It focuses on relatively isolated societies whose downfall was auto-catalyzed, mostly in the form of ecocide where a society annihilates its potential by over exploiting its natural resources. Most of the criticisms of the book appear to originate about how one case or another of collapse was in fact contaminated by outside influence.

Acemoglu and Robinson's Why Nations Fail: The Origins of Power, Prosperity, and Poverty and its sequel The Narrow Corridor: States, Societies, and the Fate of Liberty are good but not as relevent. Although they don't focus on civilizational collapse, many of their ideas seem relevant to thinking about the trajectory of civilizations. The books are sprinkled with a lot of interesting historical anecdotes about institutions and simple models about how they change, when they are destined for failure and how even if leading to ruin can stay bad for a long, long time.

It seems like there aren't many books written that take a comparative approach to studying dramatic regional declines in population / cities (my guess as a good proxy for collapse). Hope I'm wrong. There are certainly many popular cases written about local dark ages. Europe as depicted by Barbara Tuchman in A Distant Mirror: The Calamitous 14th Century is not strictly a collapsed civilization, but it's certainly tottering on the verge.

I would love to hear what other's think.