Preface -- Contents -- Braids and Braid Groups -- The Artin braid groups -- Braids and braid diagrams -- Pure braid groups -- Configuration spaces -- Braid automorphisms of free groups -- Braids and homeomorphisms -- Groups of homeomorphisms vs. configuration spaces -- Notes -- Braids, Knots, and Links -- Knots and links in three-dimensional manifolds -- Closed braids in the solid torus -- Alexander's theorem -- Links as closures of braids: an algorithm -- Markov's theorem -- Deduction of Markov's theorem from Lemma 2.11 -- Proof of Lemma 2.11 -- Notes -- Homological Representations of the Braid Groups -- The Burau representation -- Nonfaithfulness of the Burau representation -- The reduced Burau representation -- The Alexander--Conway polynomial of links -- The Lawrence--Krammer--Bigelow representation -- Noodles vs. spanning arcs -- Proof of Theorem 3.15 -- Notes -- Symmetric Groups and Iwahori--Hecke Algebras -- The symmetric groups -- The Iwahori--Hecke algebras -- The Ocneanu traces -- The Jones--Conway polynomial -- Semisimple algebras and modules -- Semisimplicity of the Iwahori--Hecke algebras -- Notes -- Representations of the Iwahori--Hecke Algebras -- The combinatorics of partitions and tableaux -- The Young lattice -- Seminormal representations -- Proof of Theorem 5.11 -- Simplicity of the seminormal representations -- Simplicity of the reduced Burau representation -- The Temperley--Lieb algebras -- Notes -- Garside Monoids and Braid Monoids -- Monoids -- Normal forms and the conjugacy problem -- Groups of fractions and pre-Garside monoids -- Garside monoids -- The braid monoid -- Generalized braid groups -- Notes -- An Order on the Braid Groups -- Orderable groups -- Pure braid groups are biorderable -- The Dehornoy order -- Nontriviality of -positive braids -- Handle reduction -- The Nielsen--Thurston approach -- Notes.

Presentations of `39`42`"613A``45`47`"603ASL2(Z) and `39`42`"613A``45`47`"603APSL2(Z) -- Notes -- Fibrations and Homotopy Sequences -- The Birman--Murakami--Wenzl Algebras -- Left Self-Distributive Sets -- LD sets, racks, and quandles -- An action of the braid monoid -- Orderable LD sets -- Notes -- References -- Index.