This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

T AKEUTVZARING. Introduction to 35 ALEXANDERI'WERMER. Several Complex Axiomatic Set Theory. 2nd ed. Variables and Banach Algebras. 3rd ed. 2 OXTOBY. Measure and Category. 2nd ed. 36 KELLEy/NAMIOKA et aL Linear 3 SCHAEFER. Topological Vector Spaces. Topological Spaces. 2nd ed. 37 MONK. Mathematical Logic. 4 HILTON/STAMMBACH. A Course in 38 GRAUERTIFRlTZSCHE. Several Complex Homological Algebra. 2nd ed. Variables. 5 MAc LANE. Categories for the Working 39 ARVESON. An Invitation to c*-Algebras. Mathematician. 2nd ed. 40 KEMENY/SNELLIKNAPP. Denumerable 6 HUGHES/PIPER. Projective Planes. Markov Chains. 2nd ed. 7 SERRE. A Course in Arithmetic. 41 ApOSTOL. Modular Functions and 8 TAKEUTVZARING. Axiomatic Set Theory. Dirichlet Series in Number Theory. 9 HUMPHREYs. Introduction to Lie Algebras 2nd ed. and Representation Theory. 42 SERRE. Linear Representations of Finite 10 COHEN. A Course in Simple Homotopy Groups. Theory. 43 GILLMAN/JERISON. Rings of Continuous 11 CONWAY. Functions of One Complex Functions. Variable I. 2nd ed. 44 KENDIG. Elementary Algebraic Geometry. 12 BEALS. Advanced Mathematical Analysis. 45 LOEVE. Probability Theory I. 4th ed. 13 ANDERSON/FULLER. Rings and Categories 46 LOEVE. Probability Theory II. 4th ed. of Modules. 2nd ed. 47 MOISE. Geometric Topology in 14 GOLUBITSKy/GUlLLEMIN. Stable Mappings Dimensions 2 and 3. and Their Singularities. 48 SACHS/WU. General Relativity for 15 BERBERIAN. Lectures in Functional Mathematicians. Analysis and Operator Theory. 49 GRUENBERG/WEIR. Linear Geometry. 16 WINTER. The Structure of Fields. 2nd ed. 17 ROSENBLATT. Random Processes. 2nd ed.

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