TITLE: General introduction to orbifolds?
QUESTION [6 upvotes]: Where should I go to learn about orbifolds?
I am interested in a general introduction that gives precise definitions and clear explanations. I have a fair background in topological and smooth manifold theory. 
Thurston's "The Geometry and Topology of Three-Manifolds" I looked at but don't like it too much because here and there it is a bit vague.
Any hints besides the Wikipedia page?

REPLY [2 votes]: When I was about to post this question on MathOverflow, I found out that it was already asked there, and the answers are really helpful.