The FIRST proposal has the goal of investigating the nature and properties of the first stars and galaxies. The project will exploit synergies between observational cosmology, galaxy formation and stellar evolution.Observations made using large ground-based and space-borne telescopes have probed cosmic history all the way from the present-day to ~ 700 million years after the Big Bang. Earlier on lies the remaining frontier, where the first stars and galaxies formed. Data collected in the last decade have revealed that the Universe at redshift ~ 7-8 is already mature, with galaxies and quasars already formed, many with metal-rich and dust-rich signatures of even earlier generations of stars. Despite these remarkable progresses, the nature of the first stars and black holes, and the impact they had on their environment and on the properties of the first galaxies and quasars remain largely unknown.The proposed research program aims to address two main scientific objectives:(1) Understand the evolution of the first metals and dust and their role in setting the characteristic masses of stars and seed black holes;(2) Assess the properties of the first galaxies and quasars.These goals will be addressed following an interdisciplinary approach which involves theoretical models of stellar evolution and nucleosynthesis, semi-analytical and numerical models of galaxy evolution, and detailed comparison with observational data from surveys at low and high redshifts. New numerical techniques will be developed, with potential applications that go beyond the primary goals of FIRST. The results will provide new insights on the nature of the first stars and galaxies and will be of important guidance for interpreting data from ongoing surveys (HST, Spitzer, IRAM, ALMA) and for the preparation of key programs with future large telescopes (ELT, JWST).