The book addresses three major topics in mathematical physics: 1. recent rigorous results in potential theory with appli- cations in particle physics, 2. analyticity in quantum field theory and its applica- tions, and 3. fundamentals and applications of the inverse problem. In addition, the book contains some contributions on questions of general interest in quantum field theory such as nonperturbative solutions of quantum chromodynamics, bifurcation theory applied to chiral symmetry, as well as exactly soluable models. The volume closes with a brief review of geometric approaches to particle physics and a phenomenological discussion of Higgs interactions. In Originalbeiträgen und Zusammenfassungen präsentiert der Band neue Resultate der Potentialtheorie mit Anwendungen in der Teilchenphysik, der Analytizität in der Quantenfeldtheorie, des inversen Problems, nicht-störungstheoretischer Lösungen in der Feldtheorie, exakt lösbare Modelle, Higgs Phänomenologie und geometrische Zugänge in der Teilchenphysik.