Abdalbagy Hatim Alshikh2018-02-052018-02-052017-11http://hdl.handle.net/123456789/10727A Thesis Submitted in Partial Fulfillment for the Degree of Master of Science in Mathematics Faculty of Mathematical Sciences and StatisticsAbstract In this work we study the theory of complex variables . Being motivated by the vast applications of this theory , we considered the analytical properties provided by the theory of complex functions in the field of electrostatics , Fluid mechanics and Harmonic analysis .We introduced the important theorems relating derivatives and integrals such as Cauchy integral formulas . We have also utilized conformal transformations in several applications such as solving Poisson equationMathematical Sciences and Statistics