This volume contains research papers and survey articles written by Beno Eckmann from 1941 to 1986. 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 them and other areas. The surveys are exemplary in terms of how they make difficult mathematical ideas easily comprehensible and accessible even to non-specialists. The topics treated here can be classified into 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 was therefore an emeritus professor.

Table of Contents:
Zur Homotopietheorie gefaserter Raume.- Uber die Homotopiegruppen von Gruppenraumen.- Systeme von Richtungsfeldern in Spharen und stetige Losungen komplexer linearer Gleichungen.- L'idee de dimension.- Stetige Losungen linearer Gleichungssysteme.- Gruppentheoretischer Beweis des Satzes von Hurwitz-Radon uber die Komposition quadratischer Formen.- Topologie und Algebra.- Uber monothetische Gruppen.- Harmonische Funktionen und Randwertaufgaben in einem Komplex.- Der Cohomologie-Ring einer beliebigen Gruppe.- Coverings and Betti numbers.- Formes differentielles et metrique hermitienne sans torsion. I. Structure complexe, formes pures.- Formes differentielles et metrique hermitienne sans torsion. II. Formes de classe k; formes analytiques.- Sur les varietes closes a metrique hermitienne sans torsion.- Quelques proprietes globales des varietes kahleriennes.- Espaces fibres et homotopie.- Sur l'integrabilite des structures presque complexes.- Complex-analytic manifolds.- On complexes with operators.- Uber injektive Moduln.- Cohomology of groups and transfer.- A class of compact, complex manifolds which are not algebraic.- Structures complexes et transformations infinitesimales.- Raume mit Mittelbildungen.- Zur Cohomologietheorie von Raumen und Gruppen.- Homotopie et dualite.- Groupes d'homotopie et dualite. Groupes absolus.- Groupes d'homotopie et dualite. Suites exactes.- Groupes d'homotopie et dualite. Coefficients.- Transgression homotopique et cohomologique.- Decomposition homologique d'un polyedre simplement connexe.- On the homology and homotopy decomposition of continuous maps.- Groupes d'homotopie et dualite.- Structure maps in group theory.- Group-like structures in general categories I. Multiplications and comultiplications.- Homotopie und Homologie.- Generalized means.- Homotopy and cohomology theory.- Unions and intersections in homotopy theory.- Composition functors and spectral sequences.- Commuting limits with colimits.- Continuous solutions of linear equations - some exceptional dimensions in topology.- Le groupe des types simples d'homotopie sur un polyedre.- Simple homotopy type and categories of fractions.- On central group extensions and homology.- On the homology theory of central group extensions: I - The commutator map and stem extensions.- On the Schur multiplicator of a central quotient of a direct product of groups.- Groups with homological duality generalizing Poincare duality.- Finiteness properties of duality groups.- Aspherical manifolds and higher-dimensional knots.- Cobordism for Poincare duality groups.- Rational representations of finite groups and their Euler class.- Two-dimensional Poincare duality groups and pairs.- On the Euler class of representations of finite groups over real fields.- Some recent developments in the homology theory of groups (Groups of finite and virtually finite dimension).- Poincare duality groups of dimension two.- Chern classes of group representations over a number field.- Plane motion groups and virtual Poincare duality of dimension two.- Poincare duality groups of dimension two, II.- Profinite Chern classes for group representations.- The p-periodicity of the groups GL (n, Os(K)) and SL(n, Os(K)).- Galois action on algebraic matrix groups, Chern classes and the Euler class.- Poincare duality groups of dimension two are surface groups.- Cyclic homology of groups and the Bass conjecture.- Notes.- I. Homotopy groups and fiber spaces.- II. Continuous solutions of linear equations.- III. Cohomology of groups.- IV. Homological algebra, transfer.- V. Duality in homotopy theory.- VI. Duality groups, Poincare duality.- Bibliography of the publications of B. Eckmann.- List of Ph.D. Theses written under the supervision of B. Eckmann.