This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics.Contents:Tunnel Number and Connected Sum of Knots (K Morimoto)Topological Imitations (A Kawauchi)Surfaces in 4-Space: A View of Normal Forms and Braidings (S Kamada)Knot Types of Satellite Knots and Twisted Knots (K Motegi)Random Knots and Links and Applications to Polymer Physics (T Deguchi & K Tsurusaki)Knots and Diagrams (L H Kauffman)On Spatial Graphs (K Taniyama)Energy and Length of Knots (G Buck & J Simon)Chern-Simons Perturbative Invariants (T Kohno)Combinatorial Methods in Dehn Surgery (C M Gordon)Readership: Mathematicians and mathematical physicists.Key Features:More than 80 years after Möbius published his book Der Barycentrische Calcul (The Barycentric Calculus) for the study of Euclidean geometry, this book provides the extension to hyperbolic geometry. As such, the book can be used by explorers to extend known results in Euclidean geometry into corresponding novel results in hyperbolic geometryThe book renews interest in barycentric calculus in Euclidean geometry, and creates interest in barycentric calculus in hyperbolic geometryThe book is of interest to every explorer who wishes to make his own discoveries of novel results in the hyperbolic geometry of Bolyai and Lobachevsky