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I want to get a basic understanding of Knot theory and since there are other people at my uni who also wish for such course I am considering of starting a reading course on Knot theory.

I have skimmed through Prasolov's & Sossinsky's: Knots,Links,Braids and 3-manifolds which is in the level of difficulty I would like, assuming basic knowledge of differential and algebraic topology , some group theory but explains or gives refference to anything else.

Any suggestions to similar texts and\or suggestions for the course would be really appreciated!

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Here are some texts that treat Knot Theory at a comparable level.

  • Lickorish - An Introduction to Knot Theory. There is a focus on geometric results in knot theory as well as the knot polynomials.
  • Rolfsen - Knots and Links. A classic and pretty much required reading for any knot theorist. It was written before the Jones polynomial was invented.
  • Murasugi - Knot Theory and its Applications. A nicely written introduction to knot theory at about the same level as Prasolov and Sossinsky. Contains more results on knot signatures than many of the other books on this list.
  • Livingston - Knot Theory. More of an introductory text than some of the others on the list. However, it is well written and often the first book I suggest to undergraduates who want to self-study knot theory.
  • Burde and Zieschang - Knots. A great book to use as reference. Contains many complete proofs that are glossed over in other texts. Perhaps a bit too dense to self-study from.

I'm sure I am omitting some great books, but this list should get you started.

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