A systematic search for disklike edge-on galaxies with a diameter larger than a=40 arcsec and major-to-minor axis ratio a/b>7 has been carried out by means of Palomar Observatory Sky Survey and ESO/SERC survey. As a result, we present new catalog of a flat galaxies (FGC) containing 4455 objects and covering about 56% of the whole sky for the first time. The catalog is assigned to study large-scale cosmic streamings and another problems of observational cosmology. Due to a better quality of the photographic emulsions used for the southern sky survey, the galaxies measured on ESO/SERC films extend to a surface magnitude slightly fainter than the same galaxies measured on POSS prints. So we present the catalog data separately for northern sky (DEC from -17.5 to +90 degrees) - FLAT GALAXY CATALOG , FGC, N = 2573 and for southern sky (DEC from -90 to -17.5 degrees) - SOUTHERN EXTENSION OF FLAT GALAXY CATALOG, FGCE, N = 1882. There are about 200 galaxies in a common region which were found and measured independently on POSS prints and ESO/SERC films. They were included in FGC, not in FGCE. The mean ratio <a(ESO)/a(POSS)> for them is equal to 1.26+/-0.4. This value is near to the result obtained by Lauberts (1982). Making some statistics it is easy to exclude FGCE galaxies with a <50arcsec to have the same depth of the sample. The Appendix to Flat Galaxy Catalog - Addendum - contains the data of 291 galaxies. They were selected in preliminary survey but rejected after more precise diameter measurements because of violation the a/b >= 7 criterion. In every case, these galaxies can be used in different observational programs.