Deriving Cosmological Parameters from the Euclid mission

The Euclid mission is a visionary project undertaken by the European Space Agency (ESA) to probe the universe's evolution and geometry by surveying the position and gravitational shape distortion of billions of galaxies. These observations bear the potential to offer unprecedented measurements of the cosmological parameters, thereby advancing our understanding of the cosmos. This work revolves around the central theme of quantifying the constraining power of the upcoming Euclid 3$\times$2pt photometric survey, accounting for several factors which have been neglected to this date in the official forecasts, especially more subtle sources of uncertainty which need to be included in the forecast (and data) analysis due to the precision of the observations. First, we include and study the impact of super-sample covariance, a source of sample variance coming from the incomplete sampling of the density and shear field Fourier modes caused by the limited survey volume. Second, we examine the effect of scale cuts, translating them from Fourier to harmonic space through the use of the BNT transform, which offers an efficient way of separating angular scales for the cosmic shear signal. This analysis allows quantifying and mitigating the bias coming from the uncertainty on our modelling of small scales. These updated forecasts, validated against the reference Euclid ones, provide insights into the expected precision achieved on the cosmological and nuisance parameters, for a variety of survey settings and for the inclusion of different realistic systematics, such as multiplicative shear bias, magnification bias, uncertainty in the mean of the redshift distribution and so on.