TITLE: Euclid with Birkhoff
QUESTION [28 upvotes]: I'm looking for a short and elementary book which does Euclidean geometry with Birkhoff's axioms.
It would be best if it would also include some topics in projective (and/or) hyperbolic geometry.
About the course. The students suppose know some basic calculus, but they did not see real proofs.
Most of the students in my course want to become math teachers.
The course description says: "Euclidean and Hyperbolic geometries and their development from postulate systems".
I choose Birkhoff's axioms since they use real numbers as a building block.
This makes it possible to do intro without cheating and without boring details.
I know some good books for school students, but I am looking for something a bit more advanced.
P.S. I want to thank everyone for their comments and answers.
As I stated in the comments, I did not find an appropriate book and wrote the lecture notes myself: Euclidean plane and its relatives; they are also available on arXiv.

REPLY [8 votes]: If you're willing to use an unpublished manuscript, from the little I've looked at it, this book by Matthew Harvey looks pretty good.  However, he uses Hilbert's axioms rather than Birkhoff's.  Jack Lee at the University of Washington is writing another book, using a variant on the SMSG postulates, designed for a geometry course for math majors who are considering teaching high school.  His book spends several chapters on hyperbolic geometry, but doesn't have any projective geometry.  The book is not publicly available, but you could email him and ask him about it.