This volume is based on the talks and lectures given by the participants of the 3-month seminar program Topology in Condensed Matter, which was held in the MPIPKS Dresden, 8 May 31 July 2002 under the scienti?c direction of Professors M. Kleman, S. Novikov, and myself. The aim of this program was to discuss recent applications of topology to several areas in condensed matter physics and related ?elds like biology. The last 30 years of the development of modern physics a?rmed two important ideas. The ?rst is the e?cient applications of topology in physics. One should mention applications in...