Acedemic advisor of the HDI Lab, prof. Eric Moulines, gave a mini-course "Introduction to Markov chains and Markov processes"
- Chapter 1 : basic definitions and constructions, invariant distribution, reversibility
- Chapter 2 : examples of Markov chains
- Chapter 18: Uniform and V-uniform ergodicity by operator methods
If you want to understand more what is a small set : Chapter 9 [first section]