Contents -- Preface -- Part 1. Abelian Covers -- Chapter 1. Links -- 1.1. Basic notions -- 1.2. The link group -- 1.3. Homology boundary links -- 1.4. Z/2Z-boundary links -- 1.5. Isotopy, concordance and I-equivalence -- 1.6. Link homotopy and surgery -- 1.7. Ribbon links -- 1.8. Link-symmetric groups -- 1.9. Link composition -- Chapter 2. Homology and Duality in Covers -- 2.1. Homology and cohomology with local coefficients -- 2.2. Covers of link exteriors -- 2.3. Some terminology and notation -- 2.4. Poincare duality and the Blanchfield pairings -- 2.5. The total linking number cover -- 2.6. The maximal abelian cover -- 2.7. Boundary 1-links -- 2.8. Concordance -- 2.9. Additivity -- 2.10. Signatures -- Chapter 3. Determinantal Invariants -- 3.1. Elementary ideals -- 3.2. The Elementary Divisor Theorem -- 3.3. Extensions -- 3.4. Reidemeister-Franz torsion -- 3.5. Steinitz-Fox-Smythe invariants -- 3.6. 1- and 2-dimensional rings -- 3.7. Bilinear pairings -- Chapter 4. The Maximal Abelian Cover -- 4.1. Metabelian groups and the Crowell sequence -- 4.2. Free metabelian groups -- 4.3. Link module sequences -- 4.4. Localization of link module sequences -- 4.5. Chen groups -- 4.6. Applications to links -- 4.7. Chen groups, nullity and longitudes -- 4.8. I-equivalence -- 4.9. The sign-determined Alexander polynomial -- 4.10. Higher dimensional links -- Chapter 5. Sublinks and Other Abelian Covers -- 5.1. The Torres conditions -- 5.2. Torsion again -- 5.3. Partial derivatives -- 5.4. The total linking number cover -- 5.5. Murasugi nullity -- 5.6. Fibred links -- 5.7. Finite abelian covers -- 5.8. Cyclic branched covers -- 5.9. Families of coverings -- Chapter 6. Twisted Polynomial Invariants -- 6.1. Definition in terms of local coefficients -- 6.2. Presentations -- 6.3. Reidemeister-Franz torsion -- 6.4. Duals and pairings -- 6.5. Reciprocity.

6.6. Applications -- Part 2. Applications: Special Cases and Symmetries -- Chapter 7. Knot Modules -- 7.1. Knot modules -- 7.2. A Dedekind criterion -- 7.3. Cyclic modules -- 7.4. Recovering the module from the polynomial -- 7.5. Homogeneity and realizing π-primary sequences -- 7.6. The Blanchfield pairing -- 7.7. Blanchfield pairings and Seifert matrices -- 7.8. Branched covers -- 7.9. Alexander polynomials of ribbon links -- Chapter 8. Links with Two Components -- 8.1. Bailey's Theorem -- 8.2. Consequences of Bailey's Theorem -- 8.3. The Blanchfield pairing -- 8.4. Links with Alexander polynomial 0 -- 8.5. 2-Component Z/2Z-boundary links -- 8.6. Topological concordance and F-isotopy -- 8.7. Some examples -- Chapter 9. Symmetries -- 9.1. Basic notions -- 9.2. Symmetries of knot types -- 9.3. Group actions on links -- 9.4. Strong symmetries -- 9.5. Semifree periods - the Murasugi conditions -- 9.6. Semifree periods and splitting fields -- 9.7. Links with infinitely many semifree periods -- 9.8. Knots with free periods -- 9.9. Equivariant concordance -- Chapter 10. Singularities of Plane Algebraic Curves -- 10.1. Algebraic curves -- 10.2. Power series -- 10.3. Puiseux series -- 10.4. The Milnor number -- 10.5. The conductor -- 10.6. Resolution of singularities -- 10.7. The Gauß-Manin connection -- 10.8. The weighted homogeneous case -- 10.9. An hermitean pairing -- Part 3. Free Covers, Nilpotent Quotients and Completion -- Chapter 11. Free Covers -- 11.1. Free group rings -- 11.2. Z[F(µ)]-modules -- 11.3. The Sato property -- 11.4. The Farber derivations -- 11.5. The maximal free cover and duality -- 11.6. The classical case -- 11.7. The case n = 2 -- 11.8. An unlinking theorem -- 11.9. Patterns and calibrations -- 11.10. Concordance -- Chapter 12. Nilpotent Quotients -- 12.1. Massey products -- 12.2. Products, the Dwyer filtration and gropes.

12.3. Mod-p analogues -- 12.4. The graded Lie algebra of a group -- 12.5. DGAs and minimal models -- 12.6. Free derivatives -- 12.7. Milnor invariants -- 12.8. Link homotopy and the Milnor group -- 12.9. Variants of the Milnor invariants -- 12.10. Solvable quotients and covering spaces -- Chapter 13. Algebraic Closure -- 13.1. Homological localization -- 13.2. The nilpotent completion of a group -- 13.3. The algebraic closure of a group -- 13.4. Complements on F(µ) -- 13.5. Other notions of closure -- 13.6. Orr invariants and cSHB-links -- Chapter 14. Disc Links -- 14.1. Disc links and string links -- 14.2. Longitudes -- 14.3. Concordance and the Artin representation -- 14.4. Homotopy -- 14.5. Milnor invariants again -- 14.6. The Gassner representation -- 14.7. High dimensions -- Bibliography -- Index.