Geometric function theory is an area of mathematics which is the study of the geometric properties of analytic functions. One of the earliest works in geometric function theory was by Riemann in 1850 when he gave the fundamental mapping theorem called the Riemann mapping theorem. In this thesis, the focus will be on complex analytic functions. The function / of a complex variable z is analytic if at points where it is defined it possesses a derivative throughout some neighborhood of that points
