Good book on non-Euclidean geometry [duplicate]

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What's a good book on non-Euclidean geometry for undergrads? Especially ones that consider hyperbolic and spherical trigonometry?

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1 Answer

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To the answers that amWhy pointed out, I'll add two more:

1. Elementary Geometry from an Advance Standpoint, by Edwin Moise. "Advanced" doesn't mean TOO advanced, although if you've had a course on real analysis and learned about Dedikind cuts, the section about Eudoxus's development of more or less the same ideas will be pretty surprising to you.

2. Foundations of Projective Geometry, by Robin Hartshorne. You'll want to have studied abstract algebra (esp. groups and fields) for this one to give full value.

--John

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