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Used Book in Good Condition
If you want to learn it systematically, consider the following:
The popular DDIA book: Designing Data-Intensive Applications gives you some insights into data systems, which are the main reason why people study those difficult distributed theories.
The underestimated textbook: Distributed Systems: An Algorithmic Approach shows you the reasoning behind the scene and gives you a taste of the algorithms used in distributed systems.
When you think it's finally over: Distributed Algorithms talks about the system models and algorithms in a more formal way.
> What research exists on how to reason about such a system?
There is a great deal of work on distributed and heterogeneous systems, because they have been the core of large-scale computing infrastructure for decades. Before diving into the research, you should be clear on what you are looking for. Are you interested in performance modelling of systems? Correctness modelling, or reasoning about the safety properties of algorithms run in the presence of distributed systems? Are you interested in liveness modelling, or reasoning about the ability of such systems to do meaningful work in all cases?
Lynch's Distributed Algorithms is the best broad book on the subject of distributed algorithms I have come across. There are many others, and where it start depends on what you know already.