Coxeter groups: reflections, rotations

This lecture provides a review of Coxeter groups, focusing on the definition of a Coxeter group as a finite group of orthogonal transformations generated by reflections. It covers the classification of finite groups of orthogonal transformations in R^3, the root system of a Coxeter group, positive roots, simple roots, and fundamental regions. The lecture also discusses simple reflections as generators of a Coxeter group and fundamental weights.