The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will soon start to scan thousands of square degrees of the northern extragalactic sky with a unique set of $56$ optical filters from a dedicated $2.55$m telescope, JST, at the Javalambre Astrophysical Observatory. Before the arrival of the final instrument (a 1.2 Gpixels, 4.2deg$^2$ field-of-view camera), the JST was equipped with an interim camera (JPAS-Pathfinder), composed of one CCD with a 0.3deg$^2$ field-of-view and resolution of 0.23 arcsec pixel$^{-1}$. To demonstrate the scientific potential of J-PAS, with the JPAS-Pathfinder camera we carried out a survey on the AEGIS field (along the Extended Groth Strip), dubbed miniJPAS. We observed a total of $sim 1$ deg$^2$, with the $56$ J-PAS filters, which include $54$ narrow band (NB, $rm{FWHM} sim 145$Angstrom) and two broader filters extending to the UV and the near-infrared, complemented by the $u,g,r,i$ SDSS broad band (BB) filters. In this paper we present the miniJPAS data set, the details of the catalogues and data access, and illustrate the scientific potential of our multi-band data. The data surpass the target depths originally planned for J-PAS, reaching $rm{mag}_{rm {AB}}$ between $sim 22$ and $23.5$ for the NB filters and up to $24$ for the BB filters ($5sigma$ in a $3$~arcsec aperture). The miniJPAS primary catalogue contains more than $64,000$ sources extracted in the $r$ detection band with forced photometry in all other bands. We estimate the catalogue to be complete up to $r=23.6$ for point-like sources and up to $r=22.7$ for extended sources. Photometric redshifts reach subpercent precision for all sources up to $r=22.5$, and a precision of $sim 0.3$% for about half of the sample. (Abridged)
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