This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held in December 2020. The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.

P. Etingof and D. Kazhdan, Characteristic functions of $p$-adic integral operatorsA. Gabrali and P. Zinn-Justin, Shuffle algebras, lattice paths and the commuting schemeS. Kolb, The bar involution for quantum symmetric pairs - hidden in plain sightT. H. Koornwinder, Charting the $q$-Askey schemeE. M. Rains, Filtered deformations of elliptic algebrasV. Regelskis and B. Vlaar, Pseudo-symmetric pairs for Kac-Moody algebrasN. Reshetikhin and J. V. Stokman, Asymptotic boundary KZB operators and quantum Calogero-Moser spin chainsM. Rosler and M. Voit, Elementary symmetric polynomials and martingales for Heckman-Opdam processesV. Schomerus, Conformal hypergeometry and integrabilityA. Varchenko, Determinant of $\mathbb{F}_p$-hypergeometric solutions under ample reductionA. Varchenko, Notes on solutions of KZ equations modulo $p^s$ and $p$-adic limit $s\to\infty$ (with an appendix by Steven Sperber and Alexander Varchenko).