This proposal focuses on the analysis of galaxy formation and evolution by use of spectroscopic data from the large datasets currently available. The project aims at developing cutting-edge techniques to extract information from galaxy spectra, with the aim of understanding the complex ("baryon") physics that transforms gas into stars, creating the galaxies we see today. The traditional approach involves an inverse problem strategy, defining a likelihood from a comparison between a range of observables and a set of parameters that define the models adopted to describe the system. These parameters, in the case of the analysis of galaxy spectra, refer to both the properties of the underlying stellar populations and the way these populations would be created and assembled during the stages of gas inflow, cooling, star formation, and feedback. The standard methodology has been very successful, allowing us to understand the general trends found in galaxies, such as the mass vs age (and metallicity) relations, the main sequence of star formation, or the dark-to-stellar matter ratio in galaxies. However, our knowledge is limited by the large degeneracies present among the parameters that describe the models. We propose here an alternative approach, where the spectra are interpreted as sets of heavily entangled information sources. Strong emphasis is made on the methodology, based on three complementary approaches involving blind source separation, information theory and machine learning techniques. They share in common the philosophy of producing data-driven research, where the observational information is explored without any a priori projection on or comparison with theoretical models. The models are used, instead, in the post-processing phase, when features are identified in galaxy spectra as being strongly representative of evolutionary trends. This project will be based on an active collaboration with expert colleagues in the different algorithmic strategies proposed, and will train two future researchers via the doctoral FPI fellowship programme.