We present the new catalog of principal galaxies (PGC2003). It constitutes the framework of the HYPERLEDA database that supersedes the LEDA one, with more data and more capabilities. The catalog is still restricted to confirmed galaxies, i.e. about one million galaxies, brighter than similar to 18 B-mag. In order to provide the best possible identification for each galaxy we give: accurate coordinates ( typical accuracy better than 2 arcsec), diameter, axis ratio and position angle. Diameters and axis ratios have been homogenized to the RC2 system at the limiting surface brightness of 25B - mag arcsec(-2), using a new method, the EPIDEMIC method. In order to provide the best designation for each galaxy, we collected the names from 50 catalogues. The compatibility of the spelling is tested against NED and SIMBAD, and, as far as possible we used a spelling compatible with both. For some cases, where no consensus exists between NED, SIMBAD and LEDA, we propose some changes that could make the spelling of names fully compatible. The full catalog is distributed through the CDS and can be extracted from HYPERLEDA.