Spectroscopic galaxy surveys are among the most powerful tools in modern cosmology, allowing us to map the large-scale structure of the Universe and constrain its fundamental parameters. In this talk, I will introduce the principles behind galaxy redshift surveys, focusing on the design and goals of the Dark Energy Spectroscopic Instrument (DESI). I will highlight key cosmological observables, including Baryon Acoustic Oscillations (BAO), and explain how DESI uses them to test models of dark energy and cosmic acceleration. I will then present recent results from DESI’s Year 1 and Year 3 analyses. Finally, I will discuss the emerging evidence for possible evolution in the dark energy equation of state and its implications for the standard cosmological model.