This overview paper presents ATOMIUM, a Large Programme in Cycle 6 with the Atacama Large Millimeter/submillimeter Array (ALMA). The goal of ATOMIUM is to understand the dynamics and the gas phase and dust formation chemistry in the winds of evolved asymptotic giant branch (AGB) and red supergiant (RSG) stars. A more general aim is to identify chemical processes applicable to other astrophysical environments. Seventeen oxygen-rich AGB and RSG stars spanning a range in (circum)stellar parameters and evolutionary phases were observed in a homogeneous observing strategy allowing for an unambiguous comparison. Data were obtained between 213.83 and 269.71 GHz at high (∼0″.025-0″.050), medium (∼0″.13-0″.24), and low (∼1″) angular resolution. The sensitivity per ∼1.3 km s<SUP>−1</SUP> channel was 1.5-5 mJy beam<SUP>−1</SUP>, and the line-free channels were used to image the millimetre wave continuum. Our primary molecules for studying the gas dynamics and dust formation are CO, SiO, AlO, AlOH, TiO, TiO<SUB>2</SUB>, and HCN; secondary molecules include SO, SO<SUB>2</SUB>, SiS, CS, H<SUB>2</SUB>O, and NaCl. The scientific motivation, survey design, sample properties, data reduction, and an overview of the data products are described. In addition, we highlight one scientific result - the wind kinematics of the ATOMIUM sources. Our analysis suggests that the ATOMIUM sources often have a slow wind acceleration, and a fraction of the gas reaches a velocity which can be up to a factor of two times larger than previously reported terminal velocities assuming isotropic expansion. Moreover, the wind kinematic profiles establish that the radial velocity described by the momentum equation for a spherical wind structure cannot capture the complexity of the velocity field. In fifteen sources, some molecular transitions other than <SUP>12</SUP>CO v = 0 J = 2 − 1 reach a higher outflow velocity, with a spatial emission zone that is often greater than 30 stellar radii, but much less than the extent of CO. We propose that a binary interaction with a (sub)stellar companion may (partly) explain the non-monotonic behaviour of the projected velocity field. The ATOMIUM data hence provide a crucial benchmark for the wind dynamics of evolved stars in single and binary star models.Read less <