Introduction to Complex Analysis in Several Variables

This thesis explores holomorphic functions in several complex variables, emphasizing the structural differences compared to the one-dimensional case. After extending classical results like the Cauchy Integral Formula and Liouville's Theorem to $n$ dimensions, the work focuses on Hartogs' Theorems. We prove that separate holomorphy implies joint holomorphy and demonstrate the Hartogs' Extension Theorem, showing that for n > 1 isolated singularities are always removable. Finally, we analyze the topological structure of the space of holomorphic functions, using Weierstrass' Theorem and Abel's Lemma to establish the properties of convergence and power series representations.