James R. Norris's Markov Chains is widely considered one of the most accessible and rigorous introductions to the field, making it a staple for advanced undergraduate and master's level students. Part of the
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If you decide to study from Norris, remember the golden rule: Work every exercise. Derive every lemma. By the time you finish Chapter 3, you will not only understand Markov chains; you will think like a probabilist. James R
To give you a taste of why the Norris PDF is so valued, consider a typical exercise (paraphrased from Chapter 1, Exercise 1.8): high-quality PDF without breaking copyright laws