The concept of "Continuous Architecture" as expressed by Erder and Pureur is not a framework or methodology, but a set of six principles and a comprehensive toolbox of good architecture practices, which are presented in a well structured and logical format. Thus the book can be read well from cover to cover as well as being used as a reference study for specific day to day problems.
After a brief introduction of the six principles, the book covers out of the view of (enterprise) architects the topics Requirement Management, Architecture Evolution, Continuous Delivery, and Architecture Validation. For each topic the authors deliver a brief explanation of the problem domain, as well as a proposed solution in the context of their Continuous Architecture concept, which is finally probed against the six principles. Followed by a fictional case study, a deeper pseudo-psychological view on the role of the Continuous Architect, Continuous Architecture in the Enterprise and Enterprise Services.
All in all the book offers a quite useful set of tools and practices without being dogmatic on their usage. Up to this point it could have been a 4-stars-rating... if they wouldn't have put the word "agile" into the subtitle of the book. This raised expectations on my side, which they didn't fulfill.
One would think, that a book about "sustainable architecture in an agile [...] world" would evolve on the concepts of the Manifesto for Agile Software Development, or at least challenge its views and concepts against it. But far from it, the only mention of the Manifesto is the statement, that the authors don't believe that the eleventh principle behind the Manifesto ("The best architectures, requirements, and designs emerge from self-organizing teams.") is applicable to the enterprise architecture world, but leads to unmanageable and wasteful amounts of refactoring.
It's also worth mentioning, that whenever the authors refer to "Agile", they really refer to the Scaled Agile Framework (SAFe), which is in my humble opinion a rather limited view on agility.