The focus of the Research Unit on Geometric Analysis at the TU Wien is twofold. On the one hand problems from integral geometry and, in particular, those related to geometric valuation theory are investigated. On the other hand isoperimetric type inequalities from convex geometry and analysis are studied and their relation to integral geometry explored. The methods applied in these investigations draw from all areas of geometry and analysis as well as probability theory and the theory of Lie groups, Lie algebras and their representations.