Geometry: Ancient and Modern

This text is a guided tour of geometry, from Euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems, and it links geometry to other branches of mathematics. It is a teaching text, with a large number of exercises woven into the exposition. Topics covered include: ruler and compass constructions
transformations
triangle and circle theorems
classification of isometries and groups of isometries in dimensions 2 and Platonic solids
conics
similarities
affine
projective and Mobius transformations
non-Euclidean geometry
projective geometry
and the beginnings of algebraic geometry.