A survey of serendipitous source performed in the very soft X-ray band (0.05-2.0 keV) using the EXOSAT imaging telescopes is presented. The survey covers 783 square degrees of high galactic latitude sky and includes 210 serendipitous sources which define a complete (flux-limited) sample. An extensive program of optical and radio observatories together with cross-correlations with catalogs of known objects lead to the identification of 200 of the 210 detected sources. The 10 remaining objects have been preliminarily classified on the basis of their X-ray to optical flux ratios, thus making the sample essentially fully identified. Twenty-three additional serendipitous sources which did not satisfy the requirements for inclusion in the complete sample were also identified during the optical observations program. The complete sample has been used to study the logN-logS relation and the average spectral slope of AGN. It is found that the logN-logS slope is consistent with that of the Einstein Extended Medium Sensitivity Survey (EMSS) and with the "Euclidean" value of 1.5. The normalization of the logN-logS is a strong function of the assumed spectral slope of AGN. Consistency with the results of the EMSS implies that the average (energy) slope of extragalactic sources in the soft X-ray band is very steep (alpha ~ 1.5). An analysis of the association between AGN detection and Galactic NH also shows that alpha is steep and inconsistent with the canonical value of 0.7. The survey was particularly successful in detecting nearby Galactic soft X-ray emitters and includes a significantly higher percentage of stars than the Einstein EMSS, five White Dwarfs, and three previously unknown AM Her type systems. The sample of sources in this catalog has been selected from the CMA database, which it has been generated using a standard processing on the LE data. The source detection algorithm used a sliding cell method. The size of the search cell is such as to maximize the sensitivity across the field of view. For more information about the LE processing see the documentation in the CMA database. This is a service provided by NASA HEASARC .