Greek geometry is one of the foundations from which modern mathematics sprang. The Greek idea of a mathematical 'proof' became the very standard of rigour for other sciences. We will explore the methods and achievements of Greek geometry through a close reading of selected texts from pure and applied Greek mathematicians, beginning with the basics of Geometry as outlined in Euclid's Elements, and then moving on to more sophisticated methods and themes in other authors. No prior knowledge of ancient or modern mathematics is required, but a willingness to learn some is essential.