Content: A knot is a smooth embedded circle in R^3. After a geometric introduction of knots our approach is rather algebraic, heavily leaning on Reidemeister moves.
Prerequisites: Little more than linear algebra plus an ability to visualise objects in 3-dimensions. Some knowledge of groups given by generators and relations, and some basic topology would be helpful.
Listed in order of accessibility:
Colin C Adams, The Knot Book, W H Freeman, 1994.
Livingston, Charles. Knot Theory Washington, DC: Math. Assoc. Amer., 1993. 240 p.
N.D. Gilbert and T. Porter, Knots and surfaces, Oxford, Oxford University Press, 1994.
Peter Cromwell, Knots and Links, CUP, 2004.
Louis H. Kauffman, Knots and physics, Singapore, Teaneck, N.J., World Scientific, 1991 Series on knots and everything, v.1.
Louis H. Kauffman, On knots, Princeton, N.J., Princeton University Press, 1987 Annals of mathematics studies, 115.
Dale Rolfsen, Knots and links, Berkeley, CA, Publish or Perish, c1976 Mathematics lecture series, 7.
Gerhard Burde, Heiner Zieschang, Knots, Berlin, New York, W. De Gruyter, 1985 De Gruyter studies in mathematics, 5.
Lectures from previous years are available on the web.