Observed galaxy number counts on the lightcone up to third order

This thesis is devoted to compute the galaxy number overdensity arising from up to third order perturbations in redshift space on cosmological scales. The aim is to compute all the general relativistic effects up to third order that arise from observing galaxies on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from peculiar velocities, Sachs-Wolfe, integrated SW effects and time-delay terms. The derivation is done in the Poisson gauge. This work follows extensively the cosmic rulers formalism used in past works on this topic, pushing it for the first time up to the third perturbative order. This result will be important for a variety of applications, such as e.g. the estimate of projection effects and possible parity violating signatures in the 3- and 4-point correlation functions of galaxies.