The millennium, together with Alan Baker's 60th birthday offered a singular occasion to organize a meeting in number theory and to bring together a leading group of international researchers in the field; it was generously supported by ETH Zurich together with the Forschungsinstitut für Mathematik. This encouraged us to work out a programme that aimed to cover a large spectrum of number theory and related geometry with particular emphasis on Diophantine aspects. Almost all selected speakers we able to accept the invitation; they came to Zurich from many parts of the world, gave lectures and contributed to the success of the meeting. The London Mathematical Society was represented by its President, Professor Martin Taylor, and it sent greetings to Alan Baker on the occasion of his 60th birthday.

This volume is dedicated to Alan Baker and it offers a panorama in number theory. It is as exciting as the scene we enjoyed, during the conference, from the cafeteria on top of ETH overlooking the town of Zurich, the lake and the Swiss mountains as well as the spectacular view that delighted us on our conference excursion to Lake Lucerne in central Switzerland. The mathematical spectrum laid before us in the lectures ranged from sophisticated problems in elementary number theory through to diophantine approximations, modular forms and varieties, metrical diophantine analysis, algebraic independence, arithmetic algebraic geometry and, ultimately, to the theory of logarithmic forms, one of the great achievements in mathematics in the last century.