Topology in condensed matter This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers on the one hand recently discovered systems such as carbon nanocrystals and on the other hand new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research some of it obtained only very recently and not yet published in monograph form. TOC:Introduction. Phason Dynamics in Aperiodic Crystals. Defects Surface Anchoring and Three Dimensional Director Fields in the Lamellar Structure of Cholesteric Liquid Crystals. Topology Quasiperiodic Functions and the Transport Phenomena. Topology in the Electron Theory of Metals. Topological Defects in Carbon Nanocrystals. Physics from Topology and Structures. Two and Three Qubits Geometry and Hopf Fibrations. Hamiltonian Monodromy as Lattice Defect. Topology of Glasses