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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?

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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.

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