This course offers a first year graduate complex analysis. In the first part of the course we will start with a review of the Residue Calculus and then cover subjects such as Winding numbers, the Argument principle, Harmonic functions and Poisson Formula, and Conformal mappings. In the second part of the course we will continue with some geometric function theory and cover 
Representation of functions by integrals, Series and products, and Analytic continuation along the curves. In the final part of the course, time permitting, we will also cover a subset of the following topics: Compact families of meromorphic functions, Approximation theorems, Special functions and Prime number theorem.