Geometric Function Theory is a branch of mathematics that studies the properties and behaviors of complex functions, particularly those that are analytic. It focuses on understanding how these functions can be represented geometrically, often using concepts from geometry and topology. This field explores various aspects, such as conformal mappings and the distortion of shapes under complex transformations. One of the key areas of interest in Geometric Function Theory is the study of holomorphic functions, which are complex functions that are differentiable in a neighborhood of every point in their domain. Researchers also investigate Riemann surfaces and analytic continuation, which help in understanding the global behavior of these functions.