The contents of this book focus on the recent investigations in molecular bi- ogywhereapplicationsoftopologyseemtobeverystimulating. Thevolumeis based on the talks and lectures given by participants of the three-month p- gram TopologyinCondensedMatter whichwasheldintheMaxPlanck- stitut fur Physik komplexer Systeme Dresden Germany 8May-31July 2002 under the scienti?c direction of Professors M. Kl´ eman S. Novikov and - self. The aim of this program was to discuss recent applications of topology to several areas in condensed matter physics and molecular biology. The ?rst volume Topology in Condensed Matter is concerned with m- ern applications of geometrical and topological techniques to such new and classic ?elds of physics like electron theory of metals theory of nano-crystals aperiodic and liquid crystals quantum computation and so on. This volume is published simultaneously in Springer Series in Solid-State Physics . The present volume gives an exposition of the role of topology in the theory of proteins and DNA. The last thirty years a?rmed very e?cient - plications of modern mathematics especially topology in physics. The union of mathematics and physics was very stimulating for both sides. On the other hand the impact of mathematics in biology has been rather limited. H- ever here also some interesting results were obtained. In particular there are applications of knot theory in the theory of circular closed DNA. The - cent discoveries in molecular biology indicate future successful applications of topology.