This 5-day workshop is part of a joint PITP/PIMS research programme. The emphasis is on topology, quantum information, spin and charge, and the general areas of strongly correlated physics and quantum magnetism. The last 2 years have seen some remarkable cross-disciplinary work between all these fields, both in mathematics and physics - these developments are almost as remarkable for their mathematical novelty as their importance for physics. The main themes to be covered in the workshop will include: The use of spin systems to realise many of the most striking new ideas in these areas. These appear in the Hubbard model and its generalisations in 1 and 2 dimensions, the 2-d Kagome spin lattice, and 3-d pyrochlore systems, in which frustration is important; other systems of interest are of course high-Tc superconductors and heavy fermions. Recent ideas also involve systems where interesting topological effects arise from spin-orbit coupling, and novel ferromagnets, like half-metallic ferromagnets and Quantum Hall bilayer ferromagnets. There has also been considerable interest in the last few years in spin liquid phases in various low-dimensional spin systems. In all of these systems, questions arise about the nature of the quasiparticles and their quantum numbers - of particular interest are the fractionalisation of quasiparticle quantum numbers, and the quasiparticle statistics. Many different scenarios have been proposed to try and unify the complex and often exotic phenomena in all these spin systems - these include quantum phase transitions, exotic quantum ordering, often non-local, and time-reversal symmetry breaking phases. There have also been interesting attempts to link this physics to quantum information theory and mathematical topology, and to to developments in string theory. relations between low-D black hole physics, open string theory, SL(2,Z) symmetry, the quantum Hall fluids, Josephson arrays, and the Hubbard model (appearing in models like the dissipative Hofstadter model, and related models). The recent study of these models has been very illuminating for condensed matter physics- some feel that it has been even more interesting for string theory. Decoherence mechanisms, and the relationship of decoherence models to models in string theory. The role of topological effects in decoherence, and the use of new models to understand decoherence in condensed matter systems and in quantum information processing. ideas for the generalisation of several condensed matter theories to string theory and quantum gravity; and analogies between the two (examples: horizon analogues, cosmic strings in superfluid He-3, and other analogies between He-3 and quantum field theories, 4-d Quantum Hall <--> quantum gravity, quantum critical phenomena and black holes, etc). Topological quantum computation, and the relationship to anyons and thence to topological field theories.