Abstract: A knot is a smooth embedding of a circle in \(R^3\). A major problem in knot theory is to classify knots. Two knots are identified if one can transform one knot to the other one without tearing.

The discovery of the Jones polynomial in 1980's has been considered as a great achievement in the classification of knots. The Jones polynomial is a sensitive knot invariant which is easy to compute. On the other hand, theories including geometry of low dimensional spaces, quantum groups and statistical mechanics meet each other because of this polynomial.

In this talk we introduce the Jones polynomial in an elementary way from two different point of views. This talk will be accessible to undergraduate students.