Abstract
This survey intends to present the basic notions of Geometric Invariant
Theory (GIT) through its paradigmatic application in the construction of the
moduli space of holomorphic vector bundles. Special attention is paid to the
notion of stability from different points of view and to the concept of maximal
unstability, represented by the Harder-Narasimhan filtration and, from which,
correspondences with the GIT picture and results derived from stratifications
on the moduli space are discussed.
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