Università Roma Tre

Euclidean geometry
Bilinear forms and quadratic forms. Diagonalization of quadratic forms. Scalar products.
The vector product operation. Euclidean spaces. Unitary operators and isometries. Isometries of plane and three-dimensional spaces. Diagonalization of symmetric operators. The complex case.

Projective geometry
Projective spaces. Affine geometry and projective geometry. Duality. Homogeneous coordinate changes
and projectivities.

Plane algebraic curves
Generality. Real algebraic curves. Classification of projective conics. Classification of affine conics
and of euclidean conics.

E. Sernesi: Geometria I, Bollati Boringhieri (1989)