"This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemann's interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written." ---Mathematical Reviews "The book is highly recommendable-for students and scientific workers-not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies." ---ZAA

• Bernhard Riemann.- Beginnings.- Doctoral Dissertation.- Privatdozent at Göttingen.- Riemann and Dirichlet.- Full Professor in Göttingen.- Last Years.- Posthumous Fate.- Topological Themes in Contemporary Physics.- Topological Structures.- The Connectivity of a Manifold and Quantization of Magnetic Flux.- Systems with Spontaneous Symmetry Breaking.- Topology and Liquid Crystals.- Theory of Gauge Fields.- Topological Particles.- Soliton Particles.- Knots, Links, and Physics.- What Next?.- A Brief Historical Survey.

"This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemann's interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written." ---Mathematical Reviews "The book is highly recommendable-for students and scientific workers-not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies." ---ZAA

• Bernhard Riemann.- Beginnings.- Doctoral Dissertation.- Privatdozent at Göttingen.- Riemann and Dirichlet.- Full Professor in Göttingen.- Last Years.- Posthumous Fate.- Topological Themes in Contemporary Physics.- Topological Structures.- The Connectivity of a Manifold and Quantization of Magnetic Flux.- Systems with Spontaneous Symmetry Breaking.- Topology and Liquid Crystals.- Theory of Gauge Fields.- Topological Particles.- Soliton Particles.- Knots, Links, and Physics.- What Next?.- A Brief Historical Survey.

"This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemann's interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written." ---Mathematical Reviews "The book is highly recommendable-for students and scientific workers-not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies." ---ZAA

• Bernhard Riemann.- Beginnings.- Doctoral Dissertation.- Privatdozent at Göttingen.- Riemann and Dirichlet.- Full Professor in Göttingen.- Last Years.- Posthumous Fate.- Topological Themes in Contemporary Physics.- Topological Structures.- The Connectivity of a Manifold and Quantization of Magnetic Flux.- Systems with Spontaneous Symmetry Breaking.- Topology and Liquid Crystals.- Theory of Gauge Fields.- Topological Particles.- Soliton Particles.- Knots, Links, and Physics.- What Next?.- A Brief Historical Survey.