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The Bialowieza workshops on Geometric Methods in Physics, taking place in the unique environment of the Bialowie a natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXII meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers of the 2013 workshop were asked to contribute and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. During the 2013 workshop the 75th birthday of Daniel Sternheimer was celebrated and on this occasion the discussion mainly focused on his contributions to mathematical physics such as deformation quantization, Poisson geometry, symplectic geometry and non commutative differential geometry.