Studies of the evolution of X-ray emission from clusters of galaxies have so far used optically discovered distant clusters then observed at X-ray wavelengths. A different approach to the study of cluster evolution is to use clusters selected directly by their X-ray emission since X-ray selection is extremely successful at discovering high redshift clusters (up to z = 0.5). The Extension of the Medium Sensitivity Survey (Gioia, Maccacaro and Wolter, 1987), a flux limited sample of serendipitous X-ray sources discovered with the Einstein IPC, has been used to select 68 optically identified clusters and 66 possible candidates (using X-ray isointensity maps and optical POSS and ESO prints). Their X-ray fluxes are in the range 10−13 – 10−12 ergs cm−2 s−1 in the 0.3–3.5 keV energy band. Few misidentifications are expected, thus the results presented here have to be considered as preliminary. This sample can be used to study the X-ray logN-logS, the cluster luminosity function and its possible evolution with cosmic time, and also to compare the properties of X-ray selected clusters with those of samples selected by other techniques. Since the identification process is still in progress, and has not proceeded completely at random, the subset of identified sources is not representative of the entire population. With this caveat in mind we have constructed the redshift and X-ray luminosity distributions for the clusters for which we have spectroscopic observations. 68% of the clusters are at z > 0.1, 34% at z > 0.2, and 12% at z > 0.3. Their X-ray luminosities range from about 3 × 1042 to 1045 ergs s−1. At present the lack of a redshift determination for many of the cluster candidates in our sample prevents us from studying the cluster luminosity function. W e can however derive their logN(>S)-logS relation.