This collection brings together papers related to the classical ideas of Sophus Lie. The present work reflects the interests of scientists associated with the International Sophus Lie Center, and provides up-to-date results in Lie groups and Lie algebras, quantum mathematics, hypergroups, homogeneous spaces, Lie superalgebras, the theory of representations and applications to differential equations and integrable systems. <br/> Among the topics that are treated are quantization of Poisson structures, applications of multivalued groups, noncommutative aspects of hypergroups, homology invariants of homogeneous spaces, generalisations of the Godbillon-Vey invariant, relations between classical problems of linear analysis and representation theory and the geometry of current groups. <br/> <em>Audience:</em> This volume will be of interest to mathematicians and physicists specialising in the theory and applications of Lie groups and Lie algebras, quantum groups, hypergroups and homogeneous spaces.