Geometric Invariant Theory Relative to a Base Curve

Abstract. These are the lecture notes to the author’s course “A relative version of Geometric Invariant Theory ” taught during the mini-school “Moduli spaces ” at the Banach Center in Warsaw which took place in April 2005. We give an account of old and new results in Geometric Invariant Theory and present recent progress in the construction of moduli spaces of vector bundles and prin-cipal bundles with extra structure (called “augmented ” or “decorated ” vector/principal bundles). Dedicated to Andrzej Białynicki-Birula on occasion of his 70th birthda