This table is the ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey Catalog. The REFLEX Cluster Survey provides information on the X-ray properties, redshifts, and some identification details of clusters in the REFLEX sample. The catalog describes a statistically complete X-ray flux-limited sample of 447 galaxy clusters above an X-ray flux of 3 x 10^-12 erg/s/cm² (0.1 to 2.4 keV) in an area of 4.24 steradians in the southern sky. The cluster candidates were first selected by their X-ray emission in the ROSAT-All Sky Survey and subsequently spectroscopically identified in the frame of an ESO key program. Previously described tests have shown that the sample is more than 90% complete and there is a conservative upper limit of 9% on the fraction of clusters with a dominant X-ray contamination from AGN. This data set is at present the largest, statistically complete X-ray galaxy cluster sample. The sample forms the basis of several cosmological studies, one of the most important applications being the assessment of the statistics of the large-scale structure of the universe and the test of cosmological models. The X-ray luminosities and other distance-dependent cluster parameters are calculated for a Lambda cosmology with a Hubble Constant H₀ of 70 km/s/Mpc, Omega_M of 0.3, and Omega_Lambda of 0.7. The CDS version of this catalog contains an additional table (reflex50.dat) with these parameters calculated for an Einstein-de Sitter universe with H₀ = 50 km/s/Mpc, Omega_M = 1.0, and Omega_Lambda = 0.0. This table was created by the HEASARC in October 2004 based on CDS tables J/A+A/425/367/reflex70.dat and J/A+A/425/367/reflex.dat. This is a service provided by NASA HEASARC .