We present the scientific program of the Spectr-M project aimed at the creation and operation of the Millimetron Space Observatory (MSO) planned for launch in the late 2020s. The unique technical capabilities of the observatory will enable broadband observations of astronomical objects from m to 10 mm wavelengths with a record sensitivity (up to Jy) in the single-dish mode and with an unprecedented high angular resolution ( s) in the ground-space very long baseline interferometer (SVLBI) regime. The program addresses fundamental priority issues in of astrophysics and physics in general that can be solved only with the MSO capabilities: 1) the study of physical processes in the early Universe up to redshifts through measuring -distortions of the cosmic microwave background (CMB) spectrum, and investigation of the structure and evolution of the Universe at redshifts by measuring -distortions of the CMB spectrum; 2) the investigation of the geometry of space-time around supermassive black holes (SMBHs) in the center of our Galaxy and M87 by imaging surrounding shadows, the study of plasma properties in the shadow formation regions, and the search for observational appearances of wormholes; 3) the study of observational appearances of the origin of life in the Universe - the search for water and biomarkers in the Galactic interstellar medium. Moreover, the technical capabilities of the MSO can help solve related problems, including the birth of the first galaxies and SMBHs ( ), alternative approaches to measuring the Hubble constant, the physics of SMBHs in ‘dusty’ galactic nuclei, the study of protoplanetary disks and water transport in them, and the study of ‘worlds with oceans’ in the Solar System.