I'm looking for an short and elementary book which does Euclidean geomety 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 wanted want to become math teachers. The course description says: "Euclidean and Hyperbolic geometries and their development from postulate systems".
I choose Birkhoff's axioms sinse they use real numbers as a building block. This makes possible to do intro without (too much) cheating and without borring details. There are I know some good books for school students, but I am looking for something bit more advanced.
P.S. I want to thank everyone for comments and answers.
As I stated in the comments, I did not find an appropriate book and wrote the lecture notes my-self. This covers the minimum of what such course should cover and at the same time this is maximum of what most students can absorb. The notes They are not very good at the moment; if I teach this course again then I will write it better. BUTavailable on arXiv, you can read it here . (All lectures are in one pdf-file and the Llecture 8 is html --- it has some java applets inside. Feel free to send corrections the link: Euclidean and suggestions.) Hyperbolic Planes.