I had ignored probability theory for many years, basically because I did not find any motivation to study it and I strongly doubted that probability would gives anything new. But now I can see how wrong and stupid I was during my undergraduate and graduate study.

I basically know nothing about probability, but I am quite familiar with real and functional analysis. In other words for me, probability is just measure theory. But this point of view wouldn't help me to understand probabilistic arguments for example random walks on groups. I want to learn about random walks on groups (over finite or Lie groups). I would be very happy and thankful if one can introduce me a reference for general theory of random walks on groups which is condense and precise, something like Atiyah-Macdonald's book in commutative algebra which is short but very precise and somehow complete.

Thank you very much