An equation of state ( EOS ) of neutron star matter , describing both the neutron star crust and the liquid core , is calculated . It is based on the effective nuclear interaction SLy of the Skyrme type , which is particularly suitable for the application to the calculation of the properties of very neutron rich matter ( Chabanat et al . 1997 , 1998 ) . The structure of the crust , and its EOS , is calculated in the T = 0 approximation , and under the assumption of the ground state composition . The crust-core transition is a very weakly first-order phase transition , with relative density jump of about one percent . The EOS of the liquid core is calculated assuming ( minimal ) npe \mu composition . Parameters of static neutron stars are calculated and compared with existing observational data on neutron stars . The minimum and maximum masses of static neutron stars are 0.094 ~ { } { M } _ { \odot } and 2.05 ~ { } { M } _ { \odot } , respectively . Effects of rotation on the minimum and the maximum mass of neutron stars are briefly discussed .