1.Basic properties of sobolev spaces. 2.Inequalities for gradients of functions that vanish on the boundary. 3.On summability of functions in the space. 4.On summability of functions in the space. 5.On continuity and boundedness of functions in sobolev spaces. 6.On functions in the spaces. 7.Certain functions spaces. Capacities and potentials. 8.On summability with respect to an arbitrary measures of functions with fractional derivatives. 9.A variant of capacity. 10.An integral inequality for functions on a cube. 11.Imbedding of the space into other functions spaces. 12.The imbedding.