I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions.Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxete…