Introduction to Vassiliev Knot Invariants

'It is clear that this book is a labour of love, and that no effort has been spared in making it a useful textbook and reference for those seeking to understand its subject. The target readership consists both of first-time learners, for whom pedagogically sound explanations and numerous well-chosen exercises are provided to enhance comprehension, and of experienced mathematicians, for whom many tables of data and readable concise guides to research literature are provided. Numerous figures are included to supplement written explanations. The content is well-modularized, in the sense that different sections of the book may be read independently of one another, and that when there is an essential dependence between sections then this fact is clearly pointed out and the relationship between the sections is explained. This, and a thorough index, combine to make this book not only a valuable textbook, but also a valuable reference.' Zentralblatt MATH

'The book's excellent preface goes on to give an in embryo characterization of the objects in the title … As being a textbook - and an excellent one - the authors take us from a dense but accessible introduction to knots as such to quantum invariants, all in the first two chapters, and then go on to Vassiliev's finite type invariants. Then we get to chord diagrams, Lie algebra connections, Kontsevich's integral, work by Drinfeld, more stuff on the Kontsevich integral, material on braids, and more. The book closes with a chapter on '[t]he space of all knots'. It's very, very attractive material.' Michael Berg, MAA Reviews