Mirrors and Reflections: The Geometry of Finite Reflection Groups

This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory
a large number of exercises at various levels of difficulty
some Euclidean geometry is included along with the theory of convex polyhedra
no prerequisites are necessary beyond the basic concepts of linear algebra and group theory
and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.