Neutrino oscillation experiments have established that at least two neutrino mass eigenstates are non-zero, measuring the two mass-squared splittings to high precision. The absolute mass scale, and in particular the mass of the lightest eigenstate, remains unknown. This is a question of fundamental importance: a vanishing lightest mass would point towards a Majorana nature for neutrinos and a seesaw origin for their masses, with implications for the identity of dark matter, whereas a non-zero value would constrain physics beyond the Standard Model in ways inaccessible to laboratory experiments alone. Cosmology is uniquely sensitive to the summed mass, through the suppression of structure growth on small scales, but only the combination of cosmological constraints on the sum with particle-physics constraints on the splittings can isolate the lightest mass. This project aims to measure the lightest neutrino mass by combining large-scale structure (LSS) surveys with cosmic microwave background (CMB) observations, exploiting the fact that these probes are sensitive to neutrinos at different cosmic epochs — as radiation in the early Universe, and as a subdominant matter component at late times. The programme uses photometric and spectroscopic galaxy clustering and weak gravitational lensing from Stage-III and Stage-IV surveys, principally the Euclid Space Telescope, the Kilo-Degree Survey (KiDS), and the Vera C. Rubin Observatory LSST, together with CMB lensing, the thermal Sunyaev–Zel'dovich effect and the integrated Sachs–Wolfe effect from Planck and subsequent CMB experiments. Cross-correlations between the LSS and CMB fields are central to the approach: they break degeneracies between the neutrino mass and other cosmological and nuisance parameters, and provide internal calibration of observational systematics. Two complementary inference strategies are pursued. The first is a tomographic two-point analysis in harmonic space, combining galaxy clustering, cosmic shear, galaxy–galaxy lensing and their cross-correlations with CMB observables at the likelihood level, alongside external constraints from neutrino oscillation experiments, supernovae and big-bang nucleosynthesis. This requires the development and validation of likelihood infrastructure incorporating physically motivated neutrino mass models, extending community frameworks including the Euclid likelihood codes (CLOE / cloelib) and the LSST-DESC framework Firecrown, in place of the degenerate mass spectrum assumed by most current analyses. The second strategy is field-level inference, in which Bayesian hierarchical models are used to infer the underlying cosmological fields directly from partial-sky, noisy observations without compression to summary statistics, building on the Almanac framework and forward models such as GLASS. Both strategies are made tractable by machine-learning acceleration: differentiable emulators for theoretical angular power spectra with non-degenerate neutrino mass spectra, generative models for the matter density field, and gradient-based samplers including Hamiltonian Monte Carlo. Together these deliver the accuracy and computational efficiency required to convert the statistical power of Stage-IV surveys into a robust measurement of the lightest neutrino mass.