We introduce the Ophiuchus DIsc Survey Employing ALMA (ODISEA), a project aiming to study the entire population of Spitzer-selected protoplanetary discs in the Ophiuchus Molecular Cloud (300 objects) from both millimetre continuum and CO isotopologues data. Here we present 1.3 mm/230 GHz continuum images of 147 targets at 0.2 arcsec (28 au) resolution and a typical rms of 0.15 mJy. We detect a total of 133 discs, including the individual components of 11 binary systems and 1 triple system. 60 of these discs are spatially resolved. We find clear substructures (inner cavities, rings, gaps, and/or spiral arms) in eight of the sources and hints of such structures in another four discs. We construct the disc luminosity function for our targets and perform preliminary comparisons to other regions. A simple conversion between flux and dust mass (adopting standard assumptions) indicates that all discs detected at 1.3 mm are massive enough to form one or more rocky planets. In contrast, only 50 discs (1/3 of the sample) have enough mass in the form of dust to form the canonical 10 M-aS center dot core needed to trigger runaway gas accretion and the formation of gas giant planets, although the total mass of solids already incorporated into bodies larger than cm scales is mostly unconstrained. The distribution in continuum disc sizes in our sample is heavily weighted towards compact discs: most detected discs have radii < 15 au, while only 23 discs of the targets) have radii > 30 au.