Geometry

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.