This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. Indeed, the evolution of transcendence into a fertile theory with numerous and widespread applications has been one of the most exciting developments of modern mathematics. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles. The work as a whole is an important contribution to mathematics and will be of considerable influence in the further direction of transcendence theory as well as an authoritative account of its current state.