## A Survey of Knot TheoryKnot theory is a rapidly developing field of research with many applications not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of knot theory from its very beginnings to today's most recent research results. The topics include Alexander polynomials, Jones type polynomials, and Vassiliev invariants. With its appendix containing many useful tables and an extended list of references with over 3,500 entries it is an indispensable book for everyone concerned with knot theory. The book can serve as an introduction to the field for advanced undergraduate and graduate students. Also researchers working in outside areas such as theoretical physics or molecular biology will benefit from this thorough study which is complemented by many exercises and examples. |

### Contents

Presentations | 7 |

Standard examples | 21 |

Compositions and decompositions | 31 |

a topological approach | 47 |

an algebraic approach | 61 |

The fundamental group | 73 |

Multivariable Alexander polynomials | 87 |

a topological approach | 99 |

a topological approach | 171 |

an algebraic approach | 189 |

Knot theory of spatial graphs | 201 |

VassilievGusarov invariants | 209 |

Appendix A The equivalence of several notions of link equivalence | 221 |

Canonical decompositions of 3manifolds | 233 |

Heegaard splittings and Dehn surgery descriptions | 241 |

Appendix F Tables of data | 253 |