Rolfsen, Knots and Links
Second printing with corrections.   xiv + 439 pages.  Paperbound only. 1990

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"The Bible of knot theory. Where many of the recent working knot theorists learned their knot   theory. A  fascinating book written in a readable style   ... "

Colin C. Adams, The Knot Book, Freeman, 1994  

Contents:
 1. Introduction.
        A. Notation and definitions
        B. Some examples of linking
 2. Codimension One and Other Matters
        A. Knots in the plane
        B. The Jordan curve theorem and chord theorem       
        C. Knots in the torus
        D. The mapping class group of the torus
        E. Solid tori
        F. Higher dimensions
        G. Connected sum and handlebodies
 3. The Fundamental Group
        A. Knot and link invariants
        B. The knot group
        C. Torus knots
        D. The Wirtinger presentation
        E. Regular projections
        F. Computations for links
        G. Chains
        H. Iterated chains and Antoine's necklace
        I. Horned spheres
        J. Applications of the fundamental group to higher-dimensional knots
        K. Unsplittable links in 4-space
        L. Generalized spinning
 4. Three-Dimensional PL Geometry
        A. Three theorems of Papakyriakopoulos
        B. The unknotting theorem
        C. Knotting of tori in the 3-sphere
        D. Knots in solid tori and companionship
 5. Seifert Surfaces
        A. Surfaces and genus
        B. Higher-dimensional Seifert surfaces
        C. Construction of the cyclic coverings of a knot complement using Seifert surfaces
        D. Linking numbers
        E. Boundary linking
 6. Finite Cyclic Coverings and Torsion Invariants
       A. Torsion numbers
        B. Calculation using Seifert surfaces
        C. Calculation using surgery in the 3-sphere
        D. Surgery description of knots
 7. Infinite Cyclic Coverings and the Alexander Invariant
       A. The Alexander invariant
        B. Seifert surfaces again
        C. Surgery again
        D. Computing the Alexander invariant from the knot group
        E. Additivity of the Alexander invariant
        F. Higher-dimensional examples: plumbing
        G. Nontrivial knots in higher dimensions with group Z
        H. Higher-dimensional knots with specified polynomial
        I. Alexander invariants of links
        J. Brunnian links in higher dimensions
 8. Matrix Invariants
        A. Seifert forms and matrices
        B. Presentation matrices
        C. Alexander matrices and Alexander polynomials
        D. The torsion invariants
        E. Signature and slice knots
        F. Concordance
 9. 3-Manifolds and Surgery on Links
        A. Introduction
        B. Lens spaces
        C. Heegaard diagrams
        D. The Poincaré conjecture, homology spheres and Dehn's construction
        E. A theorem of Bing
        F. Surgery on 3-manifolds
        G. Surgery instructions in 3-space or the 3-sphere
        H. Modification of surgery instructions
        I. The fundamental theorem of Lickorish and Wallace
        J. Knots with property P
10. Foliations, Branched Covers, Fibrations and so on
        A. Foliations
        B. Branched coverings
        C. Cyclic branched covers of the 3-sphere
        D. Cyclic covers of the 3-sphere branched over the trefoil (a lengthy example)
        E. The ubiquitous Poincaré homology sphere
        F. Other branched coverings of the 3-sphere
        G. Arbitrary 3-manifolds as branched coverings of the 3-sphere
        H. Fibred knots and links
        I. Fibering the complement of a trefoil
        J. Constructing fibrations
        K. Open book decompositions
11. A Higher-Dimensional Sampler
        A. Forming knots by adding handles
        B. Trivial sphere pairs contain nontrivial ball pairs
        C. The Smith conjecture
        D. Kervaire's characterization of knot groups
        E. Contractible 4-manifolds
Appendix A. Covering Spaces and Some Algebra in a Nutshell
Appendix B. Dehn's Lemma and the Loop Theorem
Appendix C. Table of Knots and Links

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