A

\nContext. Although dust in galaxies represents only a few percent of the total baryonic mass, it plays a crucial role in the physical processes occurring in galaxies. Studying the dust content of galaxies, particularly at high z, is therefore crucial for understanding the link between dust production, obscured star formation, and the build-up of galaxy stellar mass.\nAims. We study the dust properties (mass and temperature) of the largest Atacama Large Millimeter/submillimeter Array (ALMA)-selected sample of star-forming galaxies available from the archive (A3COSMOS), and we derive the dust mass function and dust mass density of galaxies from z = 0.5 − 6.\nMethods. We fit the spectral energy distribution (SED) with the <monospace>CIGALE</monospace> code to constrain the dust mass and temperature of the A3COSMOS galaxy sample based on the UV-to-near-infrared photometric coverage of each galaxy combined with the ALMA (and Herschel when available) coverage of the Rayleigh-Jeans tail of their dust-continuum emission. We then computed and fit the dust mass function by combining the A3COSMOS and the most recent Herschel samples in order to obtain the best estimate of the integrated dust mass density up to z ∼ 6.\nResults. The dust masses in galaxies in A3COSMOS lie between ∼108 and ∼109.5 M⊙. From the SED fitting, we were also able to derive a dust temperature. The distribution of the dust temperature peaks at ∼30 − 35 K. The dust mass function at z = 0.5 − 6 evolves with an increase in M* and a decrease in the number density (Φ*), and it agrees well with literature estimates. The dust mass density decreases smoothly in its evolution from z ∼ 0.5 to z ∼ 6, which is steeper than what is found by models at z ≳ 2.\n