The number theory group at Bristol is one of the largest in the UK, and its interests span elliptic curves, computational number theory, quantitative arithmetic geometry, quadratic forms, L-functions and the Riemann zeta function, modular and automorphic forms, Diophantine approximation, applications of the Hardy-Littlewood (circle) method and arithmetic combinatorics. The investigation of these topics draws on tools from algebraic geometry, combinatorics, dynamical systems, harmonic analysis, mathematical physics, random matrix theory and representation theory.