It is easy to point out that any function of a complex-variable can bernconsidered as a mapping from one complex plane into another. A great dealrnof attention is devoted to the study of holomorphic functions. The reason forrnthis is that many problems from the theory of holomorphic functions can bernsolved according to the following procedures;rn1. Solve the problem for the simplest possible type of domain;rn2. Express the desired solution in terms of the one already found withrnthe aid of a mapping.rnA non-constant holomorphic function maps a domain ï—ï€ ofrnthe z âˆ’ï€ planeonto another domain f (z) of the wâˆ’ï€ plane .At points wherernï€¨ï€ ï€©rn'rnf z ï‚¹ï€ 0 such a map has the remarkable property that it is conformal. Thisrnmeans that any two smooth curves intersecting in ï—ï€ map into curves whichrnintersect at the same angle in f ï€¨ï—ï€©ï€ .By means of conformal mapping,rnproblems of fluid flow, electrostatics and other fields can be mapped intornsimpler problems of the same general sort in f ï€¨ï—ï€©ï€ .Solution of the problemrnin f ï€¨ï—ï€©ï€ then solves the original problem in ï—.Conformal mapping alsorngives geometrical insight into analytic(holomorphic) questions. This seminarrnpaper includes definitions and basic properties of holomorphic functionsrn,conformal mappings(the bilinear transformations, The Schwarz-Christoffelrntransformation),Normal Families, the Riemann Mapping Theorem, whichrncharacterizes those domains that can be mapped conformally onto the unitrnopen disk and concludes with one of the consequences of the Riemannrnmapping theorem.