The volume contains the proceedings of the twenty-seventh International Conference on Operator Theory, held in Timişoara between July 2–6, 2018. It consists of a careful selection of papers authored by participants. Most of the papers are expository surveys on topics of contemporary research. The subjects covered include: (1) stochastic independence in Fock spaces; (2) positive definite functions on free groups; (3) differential geometry for \(C^{*}\)-algebras; (4) quantum information and quantum field theory; (5) partially isometric operators; (6) multi-Toeplitz operators; and (7) various ideals of operators.