The Javalambre Physics of the Accelerated Universe Astrophysical Survey (J-PAS) is a narrow band, very wide field Cosmological Survey to be carried out from the Javalambre Observatory in Spain with a purpose-built, dedicated 2.5 m telescope and a 4.7 sq.deg. camera with 1.2 Gpix. Starting in late 2016, J-PAS will observe 8500 sq.deg. of Northern Sky and measure Δz˜0.003(1+z) photo-z for 9× 107 LRG and ELG galaxies plus several million QSOs, sampling an effective volume of ˜ 14 Gpc3 up to z=1.3 and becoming the first radial BAO experiment to reach Stage IV. J-PAS will detect 7× 105 galaxy clusters and groups, setting constraints on Dark Energy which rival those obtained from its BAO measurements. Thanks to the superb characteristics of the site (seeing ˜ 0.7 arcsec), J-PAS is expected to obtain a deep, sub-arcsec image of the Northern sky, which combined with its unique photo-z precision will produce one of the most powerful cosmological lensing surveys before the arrival of Euclid. J-PAS's unprecedented spectral time domain information will enable a self-contained SN survey that, without the need for external spectroscopic follow-up, will detect, classify and measure σz˜ 0.5 redshifts for ˜ 4000 SNeIa and ˜ 900 core-collapse SNe. The key to the J-PAS potential is its innovative approach: a contiguous system of 54 filters with 145 Å width, placed 100 Å apart over a multi-degree FoV is a powerful redshift machine, with the survey speed of a 4000 multiplexing low resolution spectrograph, but many times cheaper and much faster to build. The J-PAS camera is equivalent to a 4.7 sq.deg. IFU and it will produce a time-resolved, 3D image of the Northern Sky with a very wide range of Astrophysical applications in Galaxy Evolution, the nearby Universe and the study of resolved stellar populations.