Geometric Methods in Physics XXXV : Workshop and Summer School Białowieża Poland June 26 – July 2 2016 This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics 2016. The series of Białowieża workshops attended by a community of experts at the crossroads of mathematics and physics is a major annual event in the field. The works in this book based on presentations given at the workshop are previously unpublished at the cutting edge of current research typically grounded in geometry and analysis and with applications to classical and quantum physics. In 2016 the special session Integrability and Geometry in particular attracted pioneers and leading specialists in the field. Traditionally the Białowieża Workshop is followed by a School on Geometry and Physics for advanced graduate students and early career researchers and the book also includes extended abstracts of the lecture series