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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.
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It would be best if it would also include some topics in projective and (and/or) hyperbolic geometry.

Why: I will have to teach a

About the coursein "Foundation of geometry"; . The students should have rough an idea "what is mathematical proof"suppose know some basic calculus, but they did not see real proofs.My plan is to spend 2/3 of time on Euclidean geometry then do a bit
Most of affine and projective geometry and end up at Klein model for hyperbolic geometrythe students in my course wanted to become math teachers.Surprisingly

I can not find choose Birkhoff's axioms sinse they use real numbers as a reasonable book building block. This makes possible to do intro without (or twotoo much) which would cover this subjects the way I wantcheating and without borring details. On the other hand there SO MANY There are good books on the subject that for school students, but I could easely miss oneam looking for something bit more advanced.

Most of the students in my course wanted to become math teachers; most of them saw the proofs for the first time; for most of them this is also the last time they see proofs (they are about to graduate).
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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 hyperbolic geometry.

Why: I will have to teach a course in "Foundation of geometry"; students should have rough an idea "what is mathematical proof". My plan is to spend 2/3 of time on Euclidean geometry then do a bit of affine and projective geometry and end up at Klein model for hyperbolic geometry. Surprisingly I can not find a reasonable book (or two) which would cover this subjects the way I want. On the other hand there SO MANY books on the subject that I could easely miss one.

P.S. As I stated in the comments, I 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. Most of the students want in my course wanted to become math teachers; most of them see saw the proofs for the first time; for most of them this is also the last time they see proofs (they are about to graduate).

The notes are not very good at the moment; if I teach this course again then I will write it better. BUT, 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 and suggestions.)

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