This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.
The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson.
The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).

1. A. Milas: Characters of Modules of Irrational Vertex Algebras.- 2. G. Mason: Lattice subalgebras of strongly regular vertex operator algebras.- 3. C. Dong and C. Jiang: A Characterization of the vertex operator algebra V.- 4. H. Yamauchi: Extended Griess algebras and Matsuo-Norton trace formulae.- 5. M.R. Gaberdiel and R. Volpato: Mathieu Moonshine and Orbifold K3s.- 6. M.C.N. Cheng and J.F.R. Duncan: Rademacher Sums and Rademacher Series.- 7. G. Mason and M.P. Tuite: Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II.- 8. A. Zuevsky: Twisted correlation functions on self-sewn Riemann surfaces via generalized vertex algebra of intertwiners.- 9. T. Gannon: The theory of vector-valued modular forms for the modular group.- 10. A.I. Molev and E.E. Mukhin: Yangian characters and classical W-algebras.- 11. Appendix: G. Mason: Vertex Operator Algebras, Modular Forms and Moonshine.