The study of the Large-Scale Structure of our Universe (also refered to as the filamentary Cosmic Web) is a paramount aspect of modern research in cosmology. With the advent of extremely large and precise cosmological datasets notably from the Euclid space mission, it becomes feasible to study in detail the formation of cosmic structures through gravitational instability. In particular, fine non-linear aspects of this dynamics can be studied from a theoretical point of view with the hope of detecting signatures in real observations. One of the major difficulties in this regard is probably to make the link between the observed distribution of galaxies along filaments and the underlying matter distribution for which first-principles models are known. Eventually, observing finely the "biased" cosmic web from galaxy surveys could in principle allows to probe the cosmological model (being it the concordant one or its extensions) along with the galaxy-dark matter connection. Building on recent and state of the art theoretical developments in gravitational perturbation theory and constrained random field theory, the intern will develop first-principles predictions for statistical observables (extrema counts, topological estimators, extrema correlation functions, e.g. Pogosyan et al. 2009, MNRAS 396 or Ayçoberry, Barthelemy, Codis 2024, A&A 686) of the cosmic web, applied to the actual discrete field of galaxies which only traces the total matter in a biased manner.