Best high-level introduction to classic geometry?

[desti]

Hi,

I was wondering what would be the best approach to geometry (euclidean, affine, projective) assuming you have a graduate background in linear algebra and abstract algebra? The high school curriculum in my country was pretty shallow in these subjects, none of it was covered in my undergrad, and I have noticed that they are definitely something that should be known by a grad student (because I'm specializing in algebraic geometry).

I know of Coxeter's Introduction to Geometry which I'm going to read. Any other suggestions? My classical geometry is pretty much limited to the most basic theorems of angles of triangles inscribed in a circle...

Any suggestions? Anything using a more modern approach would be great, because it helps connect the subject to stuff I know well.

 

[sundried]

Coxeter is very good. Also Bergers two volumes are very thorough. Geometric transformations by Yaglom is full of interesting problems.

For something more modern, check out Wildberger's YouTube videos on Rational trigonometry, there is lots of geometry there too.