In this chapter, we explore the phenomenon of neutrino flavour oscillations, with particular emphasis on long-baseline experiments. We numerically solve the system of coupled differential equations governing neutrino propagation in both vacuum and matter and use these solutions to compute the flavour transition probabilities and various matter effects. Building on the event generation techniques developed in previous chapters, we then apply the rejection sampling algorithm to simulate charged-current quasi-elastic (CCQE) neutrino scattering events using a far detector neutrino beam flux model, in order to reproduce the appearance spectrum of electron neutrinos emerging from a muon-neutrino-dominated beam.