Vector spaces and affine geometry:
Collinearity of three points, ratio AB/BC. Linear combinations and linear dependent set versus affine combinations and affine dependent sets. Classical theorems in affine geometry: Thales, Menelaus, Ceva, Desargues.
Affine subspaces, affine maps. Dimension of a linear subspace and of an affine subspace.
Euclidean geometry:
Scalar product, Cauchy-Schwartz inequality: norm of a vector, distance between two points, angles between two non-zero vectors. Pythagoras theorem, parallelogram law, cosine and sine rules. Elementary geometric loci.
Orthogonal transformations:
Isometries of plane (four types), Isometries of space (six types).Orthogonal bases.
Platonic polyhedra:
Euler theorem on finite planar graphs. Classification of regular polyhedra in space.
Isometries of regular polygons and regular polyhedra.
The Theory and Practice of Conformal Geometry by 
