This volume contains the proceedings of the International Colloquium on Representations and L-functions organized by the Tata Institute of Fundamental Research in January 2012, one of a series of colloquia that began in 1956. It covers a wide spectrum of mathematics, including classifications of representations, arithmeticity, the average size of the 2-Selmer group of Jacobians for certain hyperelliptic curves, certain Kuznetsov formula for symmetry types of families of L-functions, sub-convexity bounds in the level aspect, Linnik's ergodic method, beyond endoscopy, and harmonic analysis for the relative trace formula.This volume contains refereed articles by leading experts in these fields and includes original results as well as expository materials in these areas.