## ABSTRACT

In Chapter 2, we counted sets of crossings (with sign) in order to compute different linking numbers. We return to the idea of counting crossings in order to define a link invariant. Here, we fix a diagram and count the number of crossings in a designated set. Each diagram in an equivalence class determines an integer, so that we obtain a set of integers for each link. The value of the invariant is the minimum value in this set of integers.