Introduction to Euclidean Geometry

The first chapter is not about groups yet. Here, familiar concepts from school, such as reflections and rotations, are revisited and formalized. In addition, such maps are composed so that we can calculate with them. Additionally, we prove a few theorems of Euclidean geometry that clarify the structure of the Euclidean plane and higher-dimensional spaces. We want to understand geometry here in a way that allows us to grasp it algebraically.