This master thesis aims to show that the construction of some maps, called conformal maps, can be expressed by complex functions and this relation will be shown through the text. First it will be presented the spherical coordinates used for geographers and mathematicians, and the construction of a mapping of the terrestrial sphere in the plane, stereographic projection. In the following sections, they are presented: Definitions and properties of complex functions with emphasis on their geometric interpretations; Some maps generated by the exponential, logarithmic and complex trigonometric functions; The relationship between exponential function and the Mercator Map; Some characteristics of an elliptical function; The relationship between an elliptical function and the Quincuncial Pierce Map.