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. The articles here document the present state of the art and suggest possible new directions for research; they can be expected to inspire much further activity. Almost all who were invited to contribute to the volume were able to prepare an article; with very few exceptions, the promised papers were eventually submitted and the result turns out itself to be like a very colourful panoramic picture of mathematics taken on a beautiful clear day in the autumn of the year 1999.