I am looking for a good reference to learn about random walks on groups (either finite groups or Lie groups). Ideally, I would like a reference for general theory of random walks on groups that is self-contained in terms of the probability theory it relies on, while remaining condensed and precise. As an analogy, something like Atiyah-Macdonald's book in commutative algebra (i.e. short, but very precise and somehow complete) would be great.
Thank you very much.