1. Presentation and motivation

The points covered in this dossier are, in particular:

• reminders of vector geometry, such as the notions of vector space, basis and linear application;

• notions of affine space and subspace, affine applications forming the affine group, and invariants with respect to this group, in particular the detailed classification of conics and quadrics;

• notions of Euclidean space, distance, angle and orthogonality, as well as similitudes and isometries with their respective groups and invariants, in particular the detailed classification of conics and quadrics with respect to isometries.

Many disciplines, both theoretical and practical, use these concepts (cf.