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This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium onp-adic Hodge theory. This symposium was focused on recent developments inp-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.

Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic $p$, and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad...