This thesis investigates two important subjects in cosmology: the 2-point functions of the galaxy number counts, and the vorticity field of matter. In the first four chapters, we make a general treatment of the galaxy number counts, and discuss contributions to it using perturbation theory. These results are then used to construct the fully relativistic correlation function, which is valid beyond the flat-sky approximation. A publicly available code is provided for a fast and accurate numerical evaluation of the 2-point function and its multipoles, which allows us to make accurate and precise predictions on cosmological parameters from future and planned experiments. Lastly, we study the mechanism responsible for the fact that galaxies rotate, the vorticity field of matter, using numerical methods.