Quantum Groups and Noncommutative Spaces : Perspectives on Quantum Geometry This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups bridging between the algebraic representation theoretic analytic and differential geometric approaches. It also covers recent developments in Noncommutative Geometry which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max Planck Institute for Mathematics in Bonn. Contributions byTomasz Brzezinski Branimir Cacic Rita Fioresi Rita Fioresi and Fabio Gavarini Debashish Goswami Christian Kassel Avijit Mukherjee Alfons Van Daele Robert Wisbauer Alessandro Zampini The volume is aimed as introducing techniques and results on Quantum Groups and Noncommutative Geometry in a form that is accessible to other researchers in related areas as well as to advanced graduate students. The topics covered are of interest to both mathematicians and theoretical physicists. Prof. Dr. Matilde Marcolli Department of Mathematics California Institute of Technology Pasadena California USA. Dr. Deepak Parashar Cambridge Cancer Trials Centre and MRC Biostatistics Unit University of Cambridge United Kingdom.