  The main goal of this work is to present a detailed study of the foundations
of Complex Geometry, highlighting its geometrical, topological and analytical
aspects. Beginning with a preliminary material, such as the basic results on
holomorphic functions in one or more variables and the definition and first
examples of a complex manifold, we move on to an introduction to sheaf theory
and its cohomology, an essential tool to the rest of the work. After a
discussion on divisors and line bundles we turn attention to K\"ahler Geometry
and its central results, such as the Hodge Decomposition Theorem, the Hard
Lefschetz Theorem and the Lefschetz Theorem on $(1,1)$-classes. After that, we
study complex vector bundles and its geometry, focusing on the concepts of
connections, curvature and Chern classes. Finally, we finish by describing some
aspects of the topology of complex manifolds, such as the Lefschetz Hyperplane
Theorem and some of its consequences.
