After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In addition, one paper which was written in German will be translated and published in English for the first time.The sections are introduced by short explanatory notes with an emphasis on recent developments based on von Neumann's contributions. An overall picture is provided by Ulam's, one of his most intimate partners in thinking, 1958 memorial lecture. Facsimilae and translations of some of his personal letters and a newly completed bibliography based on von Neumann's own careful compilation are added.

0 Background.- 1 Fundamental Concepts.- 2 The Degree of a Map.- 3 The Fundamental Group and Covering Spaces.- 4 Manifolds.- 5 Differential Forms and Homology in Euclidean Space.- 6 Homology and Cohomology.- 7 Homotopy Classification of Maps of the Sphere.- 8 Homotopy Groups.- 9 Fibered Spaces.- 10 Fibrations and Homotopy Groups.- 11 Homotopy Theory of Fibrations.- 12 Lie Groups.- 13 Lie Algebras.- 14 Topology of Lie Groups and Homogeneous Manifolds.- 15 Geometry of Gauge Fields.- Index of Notation.

Over the past years the author has developed a quantum language going beyond the concepts used by Bohr and Heisenberg. The simple formal algebraic language is designed to be consistent with quantum theory. It differs from natural languages in its epistemology, modal structure, logical connections, and copulatives. Starting from ideas of John von Neumann and in part also as a response to his fundamental work, the author bases his approach on what one really observes when studying quantum processes. This way the new language can be seen as a clue to a deeper understanding of the concepts of quantum physics, at the same time avoiding those paradoxes which arise when using natural languages. The work is organized didactically: The reader learns in fairly concrete form about the language and its structure as well as about its use for physics.