In the 1980s Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra. In this talk I will discuss some basic properties of the Goldman bracket and its relation with Teichmüller space. I will also show how techniques from geometric group theory could be used to compute the center of the Goldman Lie algebra. I will mention some open problems related to the Goldman bracket. If time permits, I will show a method to compute geometric intersection number using Goldman bracket.