advice and for simply being a great advisor. I wish to thank Benson Farb for his hospitality during my stay at the University of Chicago and for his ongoing support afterwards.

I was supported financially by the *Graduiertenkolleg: Analytische Topologie und Metageometrie* and the *SFB 478: Geometrische Strukturen in der Mathematik*.

Many people have contributed expert knowledge and valuable advice to this project. I wish to thank Uri Bader, Pierre-Emmanuel Caprace, Ruth Charney, Walter Freyn, Theo Grundhöfer, Guntram Hainke, Clara Löh, Frederick Magata, Hendrik van Maldeghem, Lars Scheele, Petra Schwer, Markus Stroppel, Koen Thas, Anne Thomas, Alain Valette, Karen Vogtmann, Richard Weiss and Stefan Witzel for their help.

In addition to mathematical discussions with and advice from Frederick, Guntram, Lars and Petra, I would like to thank my friends for the good times we had in the last three years.

Introduction
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In the mathematical universe, this thesis is located in the area of geometric group theory, a topic at the intersection of algebra, geometry and topology. Geometric group theory studies groups by investigating their actions on ‘nice’ geometric objects. In this thesis, these geometric objects will usually be buildings or geometries related to buildings. The groups will be classical 