The ATLAS3D project is a multiwavelength survey combined with a theoretical modelling effort. The observations span from the radio to the millimetre and optical, and provide multicolour imaging, two-dimensional kinematics of the atomic (H i), molecular (CO) and ionized gas (Hβ, [O iii] and [N i]), together with the kinematics and population of the stars (Hβ, Fe5015 and Mg b), for a carefully selected, volume-limited (1.16 × 105 Mpc3) sample of 260 early-type (elliptical E and lenticular S0) galaxies (ETGs). The models include semi-analytic, N-body binary mergers and cosmological simulations of galaxy formation. Here we present the science goals for the project and introduce the galaxy sample and the selection criteria. The sample consists of nearby (D < 42 Mpc, |δ− 29°| < 35°, |b| > 15°) morphologically selected ETGs extracted from a parent sample of 871 galaxies (8 per cent E, 22 per cent S0 and 70 per cent spirals) brighter than MK < −21.5 mag (stellar mass M★≳ 6 ×109 M⊙). We analyse possible selection biases and we conclude that the parent sample is essentially complete and statistically representative of the nearby galaxy population. We present the size–luminosity relation for the spirals and ETGs and show that the ETGs in the ATLAS3D sample define a tight red sequence in a colour–magnitude diagram, with few objects in the transition from the blue cloud. We describe the strategy of the SAURON integral field observations and the extraction of the stellar kinematics with the ppxf method. We find typical 1σ errors of ΔV≈ 6 km s−1, Δσ≈ 7 km s−1, Δh3≈Δh4≈ 0.03 in the mean velocity, the velocity dispersion and Gauss–Hermite (GH) moments for galaxies with effective dispersion σe≳ 120 km s−1. For galaxies with lower σe (≈40 per cent of the sample) the GH moments are gradually penalized by ppxf towards zero to suppress the noise produced by the spectral undersampling and only V and σ can be measured. We give an overview of the characteristics of the other main data sets already available for our sample and of the ongoing modelling projects.