We present the PPAK Integral Field Spectroscopy (IFS) Nearby Galaxies Survey (PINGS), a two-dimensional spectroscopic mosaicking of 17 nearby disc galaxies in the optical wavelength range. This project represents the first attempt to obtain continuous coverage spectra of the whole surface of a galaxy in the nearby Universe. The final data set comprises more than 50 000 individual spectra, covering in total an observed area of nearly 80 arcmin2. The observations will be supplemented with broad-band and narrow-band imaging for those objects without publicly available images in order to maximize the scientific and archival values of the data set. In this paper we describe the main astrophysical issues to be addressed by the PINGS project, present the galaxy sample and explain the observing strategy, the data reduction process and all uncertainties involved. Additionally, we give some scientific highlights extracted from the first analysis of the PINGS sample. A companion paper will report on the first results obtained for NGC 628: the largest IFS survey on a single galaxy.