We present here “ The XMM-Newton Bright Serendipitous Survey ” , composed of two flux-limited samples : the XMM-Newton Bright Source Sample ( BSS , hereafter ) and the XMM-Newton “ Hard ” Bright Source Sample ( HBSS , hereafter ) having a flux limit of f _ { x } \simeq 7 \times 10 ^ { -14 } erg cm ^ { -2 } s ^ { -1 } in the 0.5-4.5 keV and 4.5-7.5 keV energy band , respectively . After discussing the main goals of this project and the survey strategy , we present the basic data on a complete sample of 400 X-ray sources ( 389 of them belong to the BSS , 67 to the HBSS with 56 X-ray sources in common ) derived from the analysis of 237 suitable XMM-Newton fields ( 211 for the HBSS ) . At the flux limit of the survey we cover a survey area of 28.10 ( 25.17 for the HBSS ) sq . deg . The extragalactic number-flux relationships ( in the 0.5-4.5 keV and in the 4.5-7.5 keV energy bands ) are in good agreement with previous and new results making us confident about the correctness of data selection and analysis . Up to now \sim 71 % ( \sim 90 % ) of the sources have been spectroscopically identified making the BSS ( HBSS ) the sample with the highest number of identified XMM-Newton sources published so far . At the X-ray flux limits of the sources studied here we found that : a ) the optical counterpart in the majority ( \sim 90 % ) of cases has a magnitude brighter than the POSS II limit ( R \sim 21 ^ { mag } ) ; b ) the majority of the objects identified so far are broad line AGN both in the BSS and in the HBSS . No obvious trend of the source spectra ( as deduced from the Hardness Ratios analysis ) as a function of the count rate is measured and the average spectra of the “ extragalactic ” population corresponds to a ( 0.5–4.5 keV ) energy spectral index of \sim 0.8 ( \sim 0.64 ) for the BSS ( HBSS ) sample . Based on the hardness ratios we infer that about 13 % ( 40 % ) of the sources in the BSS ( HBSS ) sample are described by an energy spectral index flatter than that of the cosmic X-ray background . Based on previous X-ray spectral results on a small subsample of objects we speculate that all these sources are indeed absorbed AGN with the N _ { H } ranging from a few times 10 ^ { 21 } up to few times 10 ^ { 23 } cm ^ { -2 } . We do not find strong evidence that the 4.5-7.5 keV survey is sampling a completely different source population if compared with the 0.5-4.5 keV survey ; rather we find that , as expected from the CXB synthesis models , the hard survey is simply picking up a larger fraction of absorbed AGN . At the flux limit of the HBSS sample we measure surface densities of optically type 1 and type 2 AGN of 1.63 \pm 0.25 deg ^ { -2 } and 0.83 \pm 0.18 deg ^ { -2 } , respectively ; optically type 2 AGN represent 34 \pm 9 \% of the total AGN population . Finally , we have found a clear separation , in the hardness ratio diagram and in the ( hardness ratio ) vs. ( X-ray to optical flux ratio ) diagram , between Galactic “ coronal emitting ” stars and extragalactic sources . The information and “ calibration ” reported in this paper will make the existing and incoming XMM-Newton catalogs a unique resource for astrophysical studies .