Birth events, masses and the maximum mass of Compact Stars

We give in this Chapter an overview of the problem of neutron star mass distribution, the issue of the maximum mass as inferred from the existing sample and the new gravitational wave events, and the connection with the formation events. It is shown that at least two different mass-scales (and possibly three) are favored by Bayesian and frequentist analysis, and the resulting maximum mass on empirical grounds only is $\sim 2.5 M_{\odot}$, making room for an interpretation of the lighter component of the GW190408 merger as a neutron star (as suggested by the GW event population analysis). We discuss in some length the challenges for a theoretical construction of a stiff equation of state and the status of available supernova explosions (single and binary simulations) and AIC expected to provide the masses at birth.