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The main goal of this work is to present a detailed study of the foundationsof Complex Geometry, highlighting its geometrical, topological and analyticalaspects. Beginning with a preliminary material, such as the basic results onholomorphic functions in one or more variables and the definition and firstexamples of a complex manifold, we move on to an introduction to sheaf theoryand its cohomology, an essential tool to the rest of the work. After adiscussion on divisors and line bundles we turn attention to K\"ahler Geometryand its central results, such as the Hodge Decomposition Theorem, the HardLefschetz Theorem and the Lefschetz Theorem on $(1,1)$-classes. After that, westudy complex vector bundles and its geometry, focusing on the concepts ofconnections, curvature and Chern classes. Finally, we finish by describing someaspects of the topology of complex manifolds, such as the Lefschetz HyperplaneTheorem and some of its consequences.

Fundamentos da Geometria Complexa: aspectos geom\'etricos, topol\'ogicos e anal\'iticos