Geometric function theory is found to be a hybrid or interplay of Geometry and Analysis. The cornerstone of Geometric Function Theory is the theory of univalent functions, but new related topics appeared and developed with many interesting results and applications. The major and most interesting topics are the theories of harmonic and quasi-conformal mappings and both are natural generalizations of the conformal mappings. Extremal problems of Geometric Function Theory lead naturally to the study of Special functions. Special functions have wide range of Applications in various fields like Mathematics, Physics etc.