[activatedgeek]

Markov chains in essence are simple. Instead of diverging and reading all the theory, I'd recommend do it on a need basis. Learn as you go. So pick up a problem and move ahead. I don't think it is fruitful to just learn everything about Markov Chains just for the sake of it.

Markov Chain Monte Carlo to sample from probability distributions is a good start - https://arxiv.org/abs/1206.1901 if you are into sampling.

[AlexCoventry]

Betancourt's survey is at least as good, and more up to date.

https://arxiv.org/pdf/1701.02434.pdf

[activatedgeek]

That's a great reference too for the geometric intuitions!