A quick look on Stack Exchange enabled me to discover "Geometry" from Michele Audin which is very close from what I'm expecting but there isn't the correction of the exercices.
To be more specific, I've just finished my first year in the university (Mathematics) (In France) and I'm looking for a book about two hundred pages in english about :
- Affine geometry of the plane and 3-dimensional space.
- Affine Euclidean geometry of the plane and 3-dimensional space.
- Affine Reel geometry
- Plane curve
- Space curve and surface.
And this book should contain many classics corrected exercices (exercice aiming to prove a significant mathematic result).
The best introduction to affine geometry I know Vectors and Transformations in Plane Geometry by Philippe Tondeur. Using nothing more then vector and matrix algebra in the plane, it develops basic Euclidean geometry with the transformations of similarities and isometries in the plane as completely and clearly as any book I've seen. It also gives an excellent introduction to the use of complex numbers in the plane and the Mobius transformations as unifying tools for the study of basic geometry and it's mappings. It's a wonderful book, well worth hunting down and heartily recommended.