The book consists of articles based on the XXXVII Biäowie¿a Workshop on Geometric Methods in Physics, 2018. The series of Biäowie¿a workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Biäowie¿a Workshops have been complemented by a School on Geometry and Physics comprising a series