Cosmology is going through an exciting period characterized by increasingly large and diverse surveys of the Universe. The resulting datasets contain both cosmological and astrophysical information, and provide many different perspectives on the components of the Universe and its evolution. Despite this wealth of data, there are still many open questions and unknowns. These
vary from broad questions about the nature of dark energy and dark matter, to more concrete ones, such as how fast exactly is the Universe expanding. In this thesis, we will focus on spectroscopic surveys of the large-scale structure (LSS) in the Universe, and how they are used to study these
problems.

We begin in Chapters 1-4 with an introduction of modern cosmology, focusing on the topics relevant to LSS surveys and the analysis tools used to extract cosmological information from these datasets. After that, in Chapter 5 we use the latest baryon acoustic oscillation (BAO) measurements and baryon density constraints based on big bang nucleosynthesis (BBN) to measure the expansion rate of the Universe, through the Hubble constant. This is an independent measurement that contributes to the ongoing Hubble tension debate. In Chapter 6, we perform for the first time a Bayesian analysis of the Lyman-α (Lyα) forest correlation functions in order to measure BAO. Finally, in Chapter 7 we study the possibility of an analysis of the full shape of the Lyα forest correlation functions. This would expand on BAO analyses by providing cosmological information from a broader range of scales. The next generation of cosmological surveys is just starting with
the Dark Energy Spectroscopic Instrument (DESI). Throughout this thesis, we performed multiple studies that are relevant for future cosmological analyses with DESI. These analyses will advance our physical understanding of the Universe by precisely mapping its evolution to higher redshifts than ever before.