Resources to learn Markov chains with memory or higher-order Markov chains

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What are some beginner level resources to get introduced to higher-order Markov chains or Markov chains with memory?

Clarifying the context, in case it helps. I was going through the following paper, and in section 3.1 it became hard to follow the mathematics as I have never read anything about higher-order Markov chains. I want to get comfortable with the structure of the transition matrices, the stationary aspect of higher-order Markov chains etc.