Introduction to finite Coxeter groups and their representations

Abstract: These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the conferences Recent Trends in Group Theory at IIT Bhubaneswar and the Asian - European School in Mathematics at NEHU, Shillong. The first draft was prepared by Archita Gupta (IIT Kanpur) and Sahanawaz Sabnam (NISER Bhubaneswar), to whom the author is deeply grateful. We hope these notes will be useful both for beginners and for readers who wish to study the subject further. The author also thanks the organizers and participants of the above conferences for their support and encouragement.