This expanded second edition of this work combines an account of the life and work of Bernhard Riemann with a discussion of current interaction between topology and physics.

This expanded second edition of this work combines an account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Goettingen University and developments over the last decade that connect Riemann with numerous significant ideas.

Part 1 Bernhard Riemann: beginnings
doctoral dissertation
"privatdozent" at Gottingen
Riemann and Dirichlet
full professor in Gottingen
last years
posthumous fate. Part 2 Topological themes in contemporary physics: introduction
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.