J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the symposium; the articles contained here range from overviews to reports of work still in progress, as well as a survey and complete bibliography of Adams' own work. These proceedings form an important compendium of current research in algebraic topology, and one that demonstrates the depth of Adams' many contributions to the subject. Here in the first volume the theme is mainly unstable homotopy theory, homological and categorical algebra. The second volume is oriented towards stable homotopy theory, the Steenrod algebra and the Adams spectral sequence.