Part 1. Classical geometry -- Thales and Pythagoras -- Elements of Euclid -- Conic Sections -- Further results in Euclidean geometry -- Trigonometry -- Part 2. Analytic geometry -- Descartes' geometry -- Cartesian Coordinates -- To be constructible, or not to be -- Spatial geometry and vector algebra -- Matrices and linear mappings -- Projective geometry -- Solutions to the exercises.