Intuitively, the winding number of a curve &gamma with respect to a point z0 is the number of times &gamma goes around z0 in a counter-clockwise direction.
Formally, it is defined as follows:
If &gamma is a closed curve in C and z0 is a point in C not on &gamma, then the winding number of &gamma with respect to z0 (alternately called the index of &gamma with respect to z0) is defined by the formula
The winding number is used primarily in complex analysis in the Residue theorem.