This volume contains research papers and survey articles written by Beno Eckmann from 1941 to the present day. The aim of the compilation is to provide a general view of the breadth of Eckmann''s mathematical work. His influence was particularly strong in the development of many subfields of topology and algebra, where he repeatedly pointed out close, and often surprising, connections between these, and other, areas. The surveys are exemplary in the way they make difficult mathematical ideas easily comprehensible and accessible even to non-specialists. The topics treated here can be classed in the following, not entirely unrelated areas: algebraic topology (homotopy and homology theory), algebra, group theory and differential geometry. Beno Eckmann was Professor of Mathematics at the University of Lausanne 1942-48, and Principal of the Institute for Mathematical Research at the ETH Zurich, 1964-84, where he has since been emeritus professor.