This lecture covers the inclusion of nuclear quantum effects in nonlinear spectroscopy, focusing on the double Kubo transform, multi-time correlations, symmetries, and the second-order response function. It discusses the relationship between double and single Kubo transforms, the imaginary time ordering, and the approximations using Matsubara and RPMD. The lecture also explores the phase space representation, the generalized symmetrized double Kubo transform, and the future directions in this field.