| Preface | p. ix |
| Finite and Infinite Words | p. 1 |
| Introduction | p. 1 |
| Semigroups | p. 1 |
| Words | p. 3 |
| Automata | p. 12 |
| Generating series | p. 22 |
| Symbolic dynamical systems | p. 26 |
| Unavoidable sets | p. 33 |
| Problems | p. 40 |
| Notes | p. 44 |
| Sturmian Words | p. 45 |
| Introduction | p. 45 |
| Equivalent definitions | p. 46 |
| Standard words | p. 63 |
| Sturmian morphisms | p. 83 |
| Problems | p. 101 |
| Notes | p. 108 |
| Unavoidable Patterns | p. 111 |
| Introduction | p. 111 |
| Definitions and basic properties | p. 112 |
| Deciding avoidability: the Zimin algorithm | p. 116 |
| Avoidability on a fixed alphabet | p. 123 |
| Problems | p. 131 |
| Notes | p. 133 |
| Sesquipowers | p. 135 |
| Introduction | p. 135 |
| Bi-ideal sequences | p. 136 |
| Canonical factorizations | p. 137 |
| Sesquipowers and recurrence | p. 141 |
| Extensions of a theorem of Shirshov | p. 144 |
| Finiteness conditions for semigroups | p. 149 |
| Problems | p. 159 |
| Notes | p. 162 |
| The Plactic Monoid | p. 164 |
| Introduction | p. 164 |
| Schensted's algorithm | p. 165 |
| Greene's invariants and the plactic monoid | p. 167 |
| The Robinson--Schensted--Knuth correspondence | p. 170 |
| Schur functions and the Littlewood--Richardson rule | p. 176 |
| Coplactic operations | p. 182 |
| Cyclage and canonical embeddings | p. 186 |
| Problems | p. 192 |
| Notes | p. 195 |
| Codes | p. 197 |
| Introduction | p. 197 |
| X-factorizations | p. 198 |
| Defect | p. 204 |
| More defect | p. 209 |
| A theorem of Schutzenberger | p. 221 |
| Problems | p. 224 |
| Notes | p. 227 |
| Numeration Systems | p. 230 |
| Introduction | p. 230 |
| Standard representation of numbers | p. 231 |
| Beta-expansions | p. 236 |
| U-representations | p. 248 |
| Representation of complex numbers | p. 257 |
| Problems | p. 263 |
| Notes | p. 267 |
| Periodicity | p. 269 |
| Introduction | p. 269 |
| Periods in a finite word | p. 270 |
| Local versus global periodicity | p. 283 |
| Infinite words | p. 294 |
| Problems | p. 306 |
| Notes | p. 310 |
| Centralizers of Noncommutative Series and Polynomials | p. 312 |
| Introduction | p. 312 |
| Cohn's centralizer theorem | p. 313 |
| Euclidean division and principal right ideals | p. 315 |
| Integral closure of the centralizer | p. 316 |
| Homomorphisms into k[t] | p. 319 |
| Bergman's centralizer theorem | p. 320 |
| Free subalgebras and the defect theorem | p. 322 |
| Appendix: some commutative algebra | p. 324 |
| Notes | p. 328 |
| Transformations on Words and q-Calculus | p. 330 |
| Introduction | p. 330 |
| The q-binomial coefficients | p. 332 |
| The MacMahon Verfahren | p. 334 |
| The insertion technique | p. 337 |
| The (t, q)-factorial generating functions | p. 339 |
| Words and biwords | p. 341 |
| Commutations | p. 343 |
| The two commutations | p. 345 |
| The main algorithm | p. 347 |
| The inverse of the algorithm | p. 349 |
| Statistics on circuits | p. 351 |
| Statistics on words and equidistribution properties | p. 353 |
| Problems | p. 355 |
| Notes | p. 363 |
| Statistics on Permutations and Words | p. 365 |
| Introduction | p. 365 |
| Preliminaries | p. 366 |
| Words with a given shape | p. 367 |
| Backsteps of permutations with a given shape | p. 369 |
| Inversions of permutations with a given shape | p. 372 |
| Lyndon factorization and cycles of permutations | p. 375 |
| Major index of permutations with a given cyclic type | p. 378 |
| Problems | p. 381 |
| Notes | p. 385 |
| Makanin's Algorithm | p. 387 |
| Introduction | p. 387 |
| Words and word equations | p. 389 |
| The exponent of periodicity | p. 400 |
| Boundary equations | p. 406 |
| Proof of Theorem 12.3.10 | p. 432 |
| Problems | p. 435 |
| Notes | p. 438 |
| Independent Systems of Equations | p. 443 |
| Introduction | p. 443 |
| Sets and equations | p. 444 |
| The compactness property | p. 447 |
| Independence of finite systems of equations | p. 453 |
| Semigroups without the compactness property | p. 458 |
| Semigroups with the compactness property | p. 460 |
| Problems | p. 468 |
| Notes | p. 470 |
| References | p. 473 |
| Index of Notation | p. 497 |
| General Index | p. 499 |
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