The classical theta functions are of fundamental importance in number theory, going back to their role as quasi-periodic factors of elliptic functions, Jacobi's triple product formula and consequent applications in combinatorial number theory, not to mention Riemann's wonderful proof of the functional equation of the Riemann zeta function - and much more besides!

Nowadays, this can be seen as part of a much more general theory, called the theta correspondence, which deals with automorphic forms and has deep relations to the Langlands correspondence. Points of view in the theta correspondence include analytic, algebraic and geometric methods. 

Theta functions are analytic functions, which relate to many fields of mathematics. Automorphic forms also play a pivotal role relating analysis and arithmetic through the Langlands philosophy. These automorphic forms are objects that are global in nature and have a very deep meaning from a geometric perspective at the source of important applications; they decompose however as products over all places, which provide some local associated data. This duality, between local and global, appears also in the theta correspondence. All these aspects will be covered by experts of each field, providing the unique and rare chance to get these aspects exposed all at once.