This paper describes outstanding issues in astrophysics and cosmology that can be solved by astronomical observations in a broad spectral range from far infrared to millimeter wavelengths. The discussed problems related to the formation of stars and planets, galaxies and the interstellar medium, studies of black holes and the development of the cosmological model can be addressed by the planned space observatory Millimetron (the Spectr-M project) equipped with a cooled 10-m mirror. Millimetron can operate both as a single-dish telescope and as a part of a space-ground interferometer with very long baseline.
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