Abstract: 'We introduce the notions of (semi-)stability for vector bundles and for principal bundles, and  compare them. Generally, we hope to measure how far a bundle is from being semistable, for which Harder-Narasimhan filtrations and reductions are useful.In the principal bundle case, we need to familiarize ourselves with complex reductive and semisimple groups and their root systems. We use the examples GL(r,C), SO(r,C) and Sp(2n,C).'