| Preface | p. xi |
| Abelian Covers | p. 1 |
| Links | p. 3 |
| Basic notions | p. 3 |
| The link group | p. 5 |
| Homology boundary links | p. 10 |
| Z/2Z-boundary links | p. 11 |
| Isotopy, concordance and I-equivalence | p. 13 |
| Link homotopy and surgery | p. 16 |
| Ribbon links | p. 18 |
| Link-symmetric groups | p. 24 |
| Link composition | p. 25 |
| Homology and Duality in Covers | p. 27 |
| Homology and cohomology with local coefficients | p. 27 |
| Covers of link exteriors | p. 28 |
| Some terminology and notation | p. 30 |
| Poincaré duality and the Blanchfield pairings | p. 30 |
| The total linking number cover | p. 33 |
| The maximal abelian cover | p. 35 |
| Boundary 1-links | p. 36 |
| Concordance | p. 38 |
| Additivity | p. 40 |
| Signatures | p. 42 |
| Determinantal Invariants | p. 47 |
| Elementary ideals | p. 47 |
| The Elementary Divisor Theorem | p. 54 |
| Extensions | p. 56 |
| Reidemeister-Franz torsion | p. 59 |
| Steinitz-Fox-Smythe invariants | p. 61 |
| 1- and 2-dimensional rings | p. 63 |
| Bilinear pairings | p. 66 |
| The Maximal Abelian Cover | p. 69 |
| Metabelian groups and the Crowell sequence | p. 69 |
| Free metabelian groups | p. 71 |
| Link module sequences | p. 73 |
| Localization of link module sequences | p. 76 |
| Chen groups | p. 78 |
| Applications to links | p. 78 |
| Chen groups, nullity and longitudes | p. 83 |
| I-equivalence | p. 87 |
| The sign-determined Alexander polynomial | p. 89 |
| Higher dimensional links | p. 91 |
| Sublinks and Other Abelian Covers | p. 95 |
| The Torres conditions | p. 95 |
| Torsion again | p. 100 |
| Partial derivatives | p. 103 |
| The total linking number cover | p. 105 |
| Murasugi nullity | p. 108 |
| Fibred links | p. 110 |
| Finite abelian covers | p. 113 |
| Cyclic branched covers | p. 119 |
| Families of coverings | p. 122 |
| Twisted Polynomial Invariants | p. 125 |
| Definition in terms of local coefficients | p. 125 |
| Presentations | p. 127 |
| Reidemeister-Franz torsion | p. 129 |
| Duals and pairings | p. 130 |
| Reciprocity | p. 132 |
| Applications | p. 136 |
| Applications: Special Cases and Symmetries | p. 141 |
| Knot Modules | p. 143 |
| Knot modules | p. 143 |
| A Dedekind criterion | p. 145 |
| Cyclic modules | p. 147 |
| Recovering the module from the polynomial | p. 150 |
| Homogeneity and realizing -primary sequences | p. 152 |
| The Blanchfield pairing | p. 154 |
| Blanchfield pairings and Seifert matrices | p. 159 |
| Branched covers | p. 161 |
| Alexander polynomials of ribbon links | p. 163 |
| Links with Two Components | p. 167 |
| Bailey's Theorem | p. 167 |
| Consequences of Bailey's Theorem | p. 172 |
| The Blanchfield pairing | p. 176 |
| Links with Alexander polynomial 0 | p. 178 |
| 2-Component Z/2Z-boundary links | p. 181 |
| Topological concordance and F - isotopy | p. 183 |
| Some examples | p. 184 |
| Symmetries | p. 189 |
| Basic notions | p. 189 |
| Symmetries of knot types | p. 190 |
| Group actions on links | p. 196 |
| Strong symmetries | p. 197 |
| Semifree periods - the Murasugi conditions | p. 199 |
| Semifree periods and splitting fields | p. 205 |
| Links with infinitely many semifree periods | p. 208 |
| Knots with free periods | p. 212 |
| Equivariant concordance | p. 215 |
| Singularities of Plane Algebraic Curves | p. 219 |
| Algebraic curves | p. 219 |
| Power series | p. 222 |
| Puiseux series | p. 226 |
| The Milnor number | p. 230 |
| The conductor | p. 234 |
| Resolution of singularities | p. 239 |
| The Gauß-Manin connection | p. 240 |
| The weighted homogeneous case | p. 242 |
| An hermitean pairing | p. 245 |
| Free Covers, Nilpotent Quotients and Completion | p. 247 |
| Free Covers | p. 249 |
| Free group rings | p. 249 |
| Z[F()]-modules | p. 251 |
| The Sato property | p. 257 |
| The Farber derivations | p. 259 |
| The maximal free cover and duality | p. 260 |
| The classical case | p. 264 |
| The case n = 2 | p. 266 |
| An unlinking theorem | p. 266 |
| Patterns and calibrations | p. 268 |
| Concordance | p. 270 |
| Nilpotent Quotients | p. 273 |
| Massey products | p. 273 |
| Products, the Dwyer filtration and groups | p. 275 |
| Mod-p analogues | p. 277 |
| The graded Lie algebra of a group | p. 278 |
| DGAs and minimal models | p. 279 |
| Free derivatives | p. 282 |
| Milnor invariants | p. 283 |
| Link homotopy and the Milnor group | p. 288 |
| Variants of the Milnor invariants | p. 290 |
| Solvable quotients and covering spaces | p. 291 |
| Algebraic Closure | p. 293 |
| Homological localization | p. 293 |
| The nilpotent completion of a group | p. 294 |
| The algebraic closure of a group | p. 295 |
| Complements on F() | p. 301 |
| Other notions of closure | p. 303 |
| Orr invariants and cS H B-links | p. 304 |
| Disc Links | p. 307 |
| Disc links and string links | p. 307 |
| Longitudes | p. 309 |
| Concordance and the Artin representation | p. 310 |
| Homotopy | p. 314 |
| Milnor invariants again | p. 315 |
| The Gassner representation | p. 316 |
| High dimensions | p. 319 |
| Bibliography | p. 323 |
| Index | p. 347 |
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