This is the first of two volumes constituting The Legacy of Bernhard Riemann After One Hundred and Fifty Years.Bernhard Riemann (1826–1866) possessed an original and broad vision of mathematics together with powerful skill. His work continues to influence almost all major branches of mathematics. The twenty-three papers in the two-volume set examine Riemann, his work, and his significance in the context of modern mathematical developments.Contributing authors (to the two-volume set): Michael F. Atiyah, M. V. Berry, Ching-Li Chai, Brian Conrey, Jean-Pierre Demailly, F. T. Farrell, James Glimm, David Harbater, Lizhen Ji, Jürgen Jost, Wolfgang Lück, Dan Marchesin, William H. Meeks III, Peter W. Michor, James S. Milne, Frans Oort, Joaquín Pérez, Bradley Plohr, Herman J. J. te Riele, Michael Rubinstein, Norbert Schappacher, Chi-Wang Shu, Dennis Sullivan, Claire Voisin, Shing-Tung Yau.