The analytic theory of L-functions The course will cover the theory of L-functions, from an analytic number theory perspective. Topics to be covered include: Definitions and basic properties of L-functions (Euler product, functional equation, analytic continuation) Arithmetical applications Methods of computation, such as the approximate functional equation Methods of estimation, i.e., the subconvexity problem Mean value properties, and connections to random matrix theory Distribution of zeros and nonvanishing results The textbook to be used is Iwaniec-Kowalski, Analytic Number Theory.