That's a good question. I don't think I found any useful books, although surely there are some out there. I believe I mostly read Wikipedia articles and posts on math stackexchange
That's a great reference which I hadn't seen before. Another thing to note is that it made more sense to me when I realized that (all) the states of a replicated state machine can be considered as points in a lattice. This I think was Lamport's insight. Once you make that connection then you can reason about replicated state machines in terms of lattices and posets, allowing for example proof of convergence or otherwise.