Legacy ExtraGalactic UV Survey with The Hubble Space Telescope. Stellar cluster catalogues and first insights into cluster formation and evolution in NGC 628

We report the large effort which is producing comprehensive high-level young star cluster (YSC) catalogues for a significant fraction of galaxies observed with the Legacy ExtraGalactic UV Survey (LEGUS) Hubble treasury program. We present the methodology developed to extract cluster positions, verify their genuine nature, produce multiband photometry (from NUV to NIR), and derive their physical properties via spectral energy distribution fitting analyses. We use the nearby spiral galaxy NGC628 as a test case for demonstrating the impact that LEGUS will have on our understanding of the formation and evolution of YSCs and compact stellar associations within their host galaxy. Our analysis of the cluster luminosity function from the UV to the NIR finds a steepening at the bright end and at all wavelengths suggesting a dearth of luminous clusters. The cluster mass function of NGC628 is consistent with a power-law distribution of slopes $\sim -2$ and a truncation of a few times $10^5$ M$\_\odot$. After their formation YSCs and compact associations follow different evolutionary paths. YSCs survive for a longer timeframe, confirming their being potentially bound systems. Associations disappear on time scales comparable to hierarchically organized star-forming regions, suggesting that they are expanding systems. We find mass-independent cluster disruption in the inner region of NGC628, while in the outer part of the galaxy there is little or no disruption. We observe faster disruption rates for low mass ($\leq$ $10^4$ M$\_\odot$) clusters suggesting that a mass-dependent component is necessary to fully describe the YSC disruption process in NGC628.