This volume contains the proceedings of the AMS Special Session on Inverse Problems at the AMS Fall Western Sectional Meeting, held from October 22-23, 2022, at the University of Utah, Salt Lake City, Utah. This book presents a wide variety of high-quality research in Reshetikhin-Turaev invariants, Khovanov homology, quantum groups, topological quantum field theories over algebraic number fields, nonreductive geometric invariant theory, Chebyshev polynomials, oriented bundles over oriented surfaces, and entanglement topology and tensor networks. The book may be useful for both junior and senior researchers and mathematicians in low-dimensional topology, mathematical physics, and algebraic geometry.