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Zusammenfassung This edited volume contains a mixture of expository and current research material that illustrates the far-reaching impact of 'Monstrous Moonshine' on mathematics and theoretical physics and reflects the range of research activity that has stemmed from the Moonshine conjectures. Potential directions for future development are also discussed. Inhaltsverzeichnis Preface; Schedule of talks; 1. Characters of crossed modules and premodular categories Peter Bantay; 2. On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift Jan Hendrik Bruinier and Jens Funke; 3. Ordered spanning sets for vertex operator algebras and their modules Geoffrey Buhl; 4. Friendly giant meets pointlike instantons? On a new conjecture by John McKay Anda Degeratu and Katrin Wendland; 5. Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras Chongying Dong and Zhongping Zhao; 6. Twisted modules for vertex operator algebras Benjamin Doyon; 7. Vertex operators and sporadic groups John F. Duncan; 8. The algebraic meaning of being a Hauptmodul Terry Gannon; 9. Borcherds' proof of the Conway-Norton conjecture Elizabeth Jurisich; 10. On the connection of certain Lie algebras with vertex algebras Haisheng Li; 11. Vertex operators and arithmetic: how a single photon illuminates number theory Geoffrey Mason; 12. Rational vertex operator algebras and their orbifolds Geoffrey Mason; 13. Quasi-finite algebras graded by Hamiltonian and vertex operator algebras Atushi Matsuo, Kiyokazu Nagatomo and Akihiro Tsuchiya; 14. On certain automorphic forms associated to rational vertex operator algebras Antun Milas; 15. Moonshine and group cohomology Charles B. Thomas; 16. Monstrous and generalized Moonshine and permutation orbifolds Michael P. Tuite; 17. New computations in the Monster Robert A. Wilson.
