The work presented revolves around the use of quasar spectra to probe the Universe. Absorption features in the electromagnetic spectrum of bright distant quasars by ionized hydrogen give us access to the distribution of gas in the Universe. Because the light from distant quasars is redshifted as it travels through the Universe, photons emitted with an energy below the Lyα transition will be absorbed along their journey, at the point where their wavelength has been redshifted to the transition wavelength of 1216 Å. As a result, an observed spectrum and its features, referred to as Lyα Forest, depend on the density of neutral hydrogen as a function of position along the line of sight from the quasar. Similar studies can be made with photons blueward of the emission line of the triply ionized carbon. Studying the distribution of this ionized gas on cosmological scales allows us to trace the underlying matter density field while at the same time gaining insight on the thermal state of the intergalactic medium and its enrichment processes. We also present an analytical framework to understand the effects of a fluctuating intensity of the cosmic ionizing background on the correlations of the Lyα Forest transmission fraction measured in quasar spectra.