This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. It is the first of three volumes dedicated to p-adic Hodge theory.

Notes on the Ainf-cohomology of Integral p-adic Hodge theory (M. Morrow).- On the cohomology of the affine space (P. Colmez, W. Nizio).- Arithmetic Chern-Simons Theory II (H.-J. Chung, D. Kim, M. Kim, J. Park, H. Yoo).- Some ring-theoretic properties of Ainf (K.S. Kedlaya).- Sure uneq-déformation locale de la théorie de Hodge non-abélienne en caractéristique positive (M. Gros).- Crystalline Zp-representations and Ainf-representations with Frobenius (T. Tsuji).