A note on Haar Measure

1. When I was young, I was told, there is a proof of the existence of Haar measure without using the axiom of choice. Here it is. 

2. It contatins some examples (in exercise).

3. The references are not complete. I referred also Folland Real analysis. 

4. Maybe the citation of Urysohn lemma is not exact, it should be "Urysohn lemma and uniformly continuity,".